content: <PAGE>   1
       As filed with the Securities and Exchange Commission on January 5, 1999
                                              Registration Statement No. 333-
  ================================================================================
  
  
                         SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                                  ---------------
  
                                      FORM S-8
                               REGISTRATION STATEMENT
                                        UNDER
                             THE SECURITIES ACT OF 1933
  
                                  ---------------
  
                             BRIGHAM EXPLORATION COMPANY
               (Exact name of registrant as specified in its charter)
  
                       DELAWARE                           75-2692967
            (State or other jurisdiction      (I.R.S. Employer Identification No.)
          of incorporation or organization)         
  
   
  
  6300 BRIDGE POINT PARKWAY, BUILDING 2, SUITE 500
                    AUSTIN, TEXAS
      (Address of principal executive offices)
  
  
                        78730
                      (Zip Code)
  
                                    -------------
  
                                    BRIGHAM, INC.
                                     401(k) PLAN
              (AS AMENDED AND RESTATED EFFECTIVE AS OF JANUARY 1, 1999)
                              (Full title of the Plan)
  
                                    -------------
  
                                   Ben. M. Brigham
                         President, Chief Executive Officer
                              and Chairman of the Board
                             Brigham Exploration Company
                  6300 Bridge Point Parkway, Building 2, Suite 500
                                 Austin, Texas 78730
                                   (512) 427-3300
              (Name, address and telephone number of agent for service)
  
                                      Copy to:
                                   Joe Dannenmaier
                               Thompson & Knight, P.C.
                           1700 Pacific Avenue, Suite 3300
                                 Dallas, Texas 75201
                                   (214) 969-1700
  
                                    -------------
                           CALCULATION OF REGISTRATION FEE
  
  <TABLE>
  <CAPTION>
  ====================================================================================================================================
              Title of securities to be          Amount to be    Proposed maximum offering    Proposed maximum           Amount of
                     registered                   registered        price per share(1)    aggregate offering price(1) registration fee
  ------------------------------------------------------------------------------------------------------------------------------------
  <S>                                         <C>                   <C>                   <C>                             <C>
  
  Common Stock, par value $.01 per share .... 300,000 shares (2)          $4.88                 $1,464,000                $407
  ------------------------------------------------------------------------------------------------------------------------------------
  Interests in the 401(k) Plan of            
  Brigham, Inc. .............................         (3)                   (4)                     (4)                    (4)
  ====================================================================================================================================
  </TABLE>
  
  (1)      Estimated solely for the purpose of calculating the registration fee
           pursuant to Rule 457(h) under the Securities Act of 1933 (the
           "Securities Act") and based on the average of the high and low prices
           of the common stock reported on The Nasdaq Stock Markets' National
           Market on December 30, 1998.
  (2)      If, as a result of stock splits, stock dividends or similar
           transactions, the number of securities purported to be registered on
           this Registration Statement changes, the provisions of Rule 416 shall
           apply to this Registration Statement, and this Registration Statement
           shall be deemed to cover the additional securities resulting from the
           split of, or the dividend on, the securities covered by this
           Registration Statement.
  (3)      Pursuant to Rule 416(c) under the Securities Act, this Registration
           Statement also covers an indeterminate amount of plan interests to be
           offered or sold pursuant to the Brigham Inc. 401(k) Plan.
  (4)      Pursuant to Rule 457(h)(2) under the Securities Act, no separate fee is
           required to register plan interests.
  
  ================================================================================
  
  
  
  <PAGE>   2
  
  
  
                                       PART I
  
                INFORMATION REQUIRED IN THE SECTION 10(a) PROSPECTUS
  
  Item 1.      Plan Information.*
  
  Item 2.      Registrant Information and Employee Plan Annual Information.*
  
  -------------
  
  *        Information required by Part I to be contained in the Section 10(a)
           prospectus is omitted from this Registration Statement in accordance
           with Rule 428 under the Securities Act of 1933 and the Note to Part I
           of Form S-8.
  
  
  
  
  
  <PAGE>   3
  
  
  
                                       PART II
  
                 INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
  
  Item 3.      Incorporation of Documents by Reference.
  
         The following documents have been filed by the Registrant with the
  Securities and Exchange Commission and are incorporated by reference in this
  Registration Statement:
  
         (1)    The Company's Annual Report on Form 10-K for the fiscal year ended
                December 31, 1997;
  
         (2)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                September 30, 1998;
  
         (3)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                June 30, 1998;
  
         (4)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                March 31, 1998;
  
         (4)    The Company's Current Report on Form 8-K (Date of Event: November
                12, 1997) filed January 23, 1998;
  
         (5)    The description of the Company's Common Stock, $.01 par value per
                share, contained in the Registration Statement on Form 8-A
                (Registration No. 000-22433) of the Company heretofore filed with
                the Commission, including any amendments or reports filed for the
                purpose of updating such description.
  
         In addition, all documents filed by the Registrant pursuant to Sections
  13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934 subsequent to
  the date of this Registration Statement and prior to the filing of a
  post-effective amendment which indicates that all securities offered have been
  sold or which deregisters all securities then remaining unsold shall be deemed
  to be incorporated by reference in this Registration Statement and to be a part
  hereof from the date of filing of such documents. Any statement contained in a
  document incorporated or deemed to be incorporated by reference herein shall be
  deemed to be modified or superseded for purposes of this Registration Statement
  to the extent that a statement contained herein or in any other subsequently
  filed document which also is or is deemed to be incorporated by reference herein
  modifies or supersedes such statement. Any statement so modified or superseded
  shall not be deemed, except as so modified or superseded, to constitute a part
  of this Registration Statement. Upon the written or oral request of any person
  to whom a copy of this Registration Statement has been delivered, the Company
  will provide without charge to such person a copy of any and all documents
  (excluding exhibits thereto unless such exhibits are specifically incorporated
  by reference into such documents) that have been incorporated by reference into
  this Registration Statement but not delivered herewith. Requests for such
  documents should be addressed to Brigham Exploration Company, 6300 Bridge Point
  Parkway, Building 2, Suite 500, Austin, Texas 78730, Attention: Corporate
  Secretary, (512) 427-3300.
  
  
  Item 4.      Description of Securities.
  
         Not Applicable.
  
  
  Item 5.      Interests of Named Experts and Counsel.
  
         Not Applicable.
  
  
  Item 6.      Indemnification of Directors and Officers.
  
         In accordance with Section 102(b)(7) of the Delaware General Corporation
  Law ("DGCL") the Registrant's Certificate of Incorporation includes a provision
  that, to the fullest extent permitted by law, eliminates the personal liability
  of members of its board of directors to the corporation or its stockholders for
  monetary damages for breach of fiduciary duty as a director. Such provision does
  not eliminate or limit the liability of a director (1) for any breach of a
  director's duty of loyalty to the corporation or its stockholders, (2) for acts
  or omissions not in good faith or which involve intentional misconduct or a
  
  
                                        II-1
  
  <PAGE>   4
  
  
  
  knowing violation of a law, (3) for paying an unlawful dividend or approving an
  illegal stock repurchase (as provided in Section 174 of the DGCL), or (4) for
  any transaction from which the director derived an improper personal benefit.
  
         Under Section 145 of the DGCL, the Registrant has the power to indemnify
  any person who was or is a party or is threatened to be made a party to any
  threatened, pending or completed action, suit or proceeding (other than an
  action by or in the right of the corporation) by reason of the fact that the
  person is or was a director, officer, employee or agent of any corporation,
  partnership, joint venture, trust or other enterprise, against any and all
  expenses (including attorneys' fees), judgments, fines and amounts paid in
  settlement and reasonably incurred in connection with such action, suit or
  proceeding. The power to indemnify applies only if the person acted in good
  faith and in a manner he reasonably believed to be in or not opposed to the best
  interests of the corporation, and with respect to any criminal action or
  proceeding, had no reasonable cause to believe the person's conduct was
  unlawful.
  
         In the case of an action by or in the right of the Registrant, no
  indemnification may be made with respect to any claim, issue or matter as to
  which such person shall have been adjudged to be liable to the corporation
  unless and only to the extent that the court of chancery or the court in which
  such action or suit was brought shall determine that despite the adjudication of
  liability such person is fairly and reasonably entitled to indemnity for such
  expenses which the court shall deem proper. Section 145 of the DGCL further
  provides that to the extent a director or officer of the Registrant has been
  successful in the defense of any action, suit or proceeding referred to above or
  in the defense of any claim, issue or matter therein, he shall be indemnified
  against expenses (including attorney's fees) actually and reasonably incurred by
  him in connection therewith.
  
         The Registrant also has the power to purchase and maintain insurance on
  behalf of any person covering any liability incurred by such person in his
  capacity as a director, officer, employee or agent of the corporation, or
  arising out of his status as such, whether or not the corporation would have the
  power to indemnify him against such liability.
  
         The Certificate of Incorporation and Bylaws provide that the Registrant
  will indemnify its officers and directors and former officers and directors
  against any expenses, judgments or settlement payments sustained or paid by such
  persons as a result of having acted as an officer or director of the Registrant,
  or, at the request of the Registrant, as an officer, director, agent or employee
  of another business entity. The Certificate of Incorporation and Bylaws further
  provide that the Registrant may, by action of its Board of Directors, provide
  indemnification to employees and agents of the Registrant, individually or as a
  group, with the same scope and effect as the indemnification of directors and
  officers.
  
         The Registrant has entered into an Indemnity Agreement with each of its
  executive officers which provides for the indemnification in certain instances
  against liability and expenses incurred in connection with proceedings brought
  by or in the right of the Registrant or by third parties by reason of the person
  serving as an officer or direction of the Registrant.
  
  Item 7.      Exemption from Registration Claimed.
  
         Not Applicable.
  
  
  Item 8.      Exhibits.
  
         The following documents are filed as exhibits to this Registration
  Statement:
  
                4.1   Brigham, Inc. 401(k) Plan.
  
                5.1   Opinion of Thompson & Knight, A Professional Corporation.
  
                23.1  Consent of Thompson & Knight, A Professional Corporation
                      (included in the opinion of Thompson & Knight, P.C. filed
                      herewith as Exhibit 5.1).
  
                23.2  Consent of PricewaterhouseCoopers LLP.
  
                24.1  Power of Attorney (included on signature page of this
                      Registration Statement).
  
  
  
                                        II-2
  
  <PAGE>   5
  
  
  
  Item 9.      Undertakings.
  
         The Registrant hereby undertakes:
  
               (1) To file, during any period in which offers or sales are being
         made, a post-effective amendment to this Registration Statement:
  
                   (i) To include any prospectus required by Section 10(a)(3) of
               the Securities Act of 1933;
  
                   (ii) To reflect in the prospectus any facts or events arising
               after the effective date of this Registration Statement (or the
               most recent post-effective amendment thereof) which, individually
               or in the aggregate, represent a fundamental change in the
               information set forth in this Registration Statement.
               Notwithstanding the foregoing, any increase or decrease in volume
               of securities offered (if the total dollar value of securities
               offered would not exceed that which was registered) and any
               deviation from the low or high end of the estimated maximum
               offering range may be reflected in the Form of prospectus filed
               with the Commission pursuant to Rule 424(b) if, in the aggregate,
               the changes in volume and price represent no more than a 20% change
               in the maximum aggregate offering price set forth in the
               "Calculation of Registration Fee" table in the effective
               registration statement; and
  
                   (iii) To include any material information with respect to the
               plan of distribution not previously disclosed in this Registration
               Statement or any material change to such information in this
               Registration Statement;
  
         provided, however, that paragraphs (1)(i) and (1)(ii) do not apply if the
         information required to be included in a post-effective amendment by
         those paragraphs is contained in periodic reports filed by the Registrant
         pursuant to Section 13 or Section 15(d) of the Securities Exchange Act of
         1934 that are incorporated by reference in this Registration Statement.
  
               (2) That, for the purpose of determining any liability under the
         Securities Act of 1933, each such post-effective amendment shall be
         deemed to be a new registration statement relating to the securities
         offered therein, and the offering of such securities at that time shall
         be deemed to be the initial bona fide offering thereof.
  
               (3) To remove from registration by means of a post-effective
         amendment any of the securities being registered which remain unsold at
         the termination of the offering.
  
               (4) That, for purposes of determining any liability under the
         Securities Act of 1933, each filing of the Registrant's annual report
         pursuant to Section 13(a) or Section 15(d) of the Securities Exchange Act
         of 1934 that is incorporated by reference in this Registration Statement
         shall be deemed to be a new registration statement relating to the
         securities offered therein, and the offering of such securities at that
         time shall be deemed to be the initial bona fide offering thereof.
  
               (5) Insofar as indemnification for liabilities arising under the
         Securities Act of 1933 may be permitted to directors, officers and
         controlling persons of the Registrant pursuant to the foregoing
         provisions, or otherwise, the Registrant has been advised that in the
         opinion of the Securities and Exchange Commission such indemnification is
         against public policy as expressed in the Act and is, therefore,
         unenforceable. In the event that a claim for indemnification against such
         liabilities (other than the payment by the Registrant of expenses
         incurred or paid by a director, officer or controlling person of the
         Registrant in the successful defense of any action, suit or proceeding)
         is asserted by such director, officer or controlling person in connection
         with the securities being registered, the Registrant will, unless in the
         opinion of its counsel the matter has been settled by controlling
         precedent, submit to a court of appropriate jurisdiction the question
         whether such indemnification by it is against public policy as expressed
         in the Act and will be governed by the final adjudication of such issue.
  
  
  
                                        II-3
  
  <PAGE>   6
  
  
  
                                     SIGNATURES
  
         Pursuant to the requirements of the Securities Act of 1933, the
  Registrant certifies that it has reasonable grounds to believe that it meets all
  of the requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in the City of Austin and State of Texas on the 31 day of December,
  1998.
  
                                     BRIGHAM EXPLORATION COMPANY
  
  
                                     By:   /s/ Ben M. Brigham
                                           -------------------------------------
                                           Ben M. Brigham, President, 
                                           Chief Executive Officer
                                           and Chairman of the Board
  
  
                                  POWER OF ATTORNEY
  
         KNOW ALL MEN BY THESE PRESENTS, that the undersigned directors and
  officers of Brigham Exploration Company, a Delaware corporation, which is filing
  a Registration Statement on Form S-8 with the Securities and Exchange Commission
  under the provisions of the Securities Act of 1933, as amended, hereby
  constitute and appoint Ben M. Brigham and Anne L. Brigham, and each of them, his
  true and lawful attorneys-in-fact and agents, with full power of substitution
  and resubstitution, for him and in his name, place and stead, in any and all
  capacities, to sign such Registration Statement and any or all amendments to the
  Registration Statement, and all other documents in connection therewith to be
  filed with the Securities and Exchange Commission, granting unto said
  attorneys-in-fact and agents, and each of them, full power and authority to do
  and perform each and every act and thing requisite and necessary to be done in
  and about the premises, as fully to all intents and purposes as he might or
  could do in person, hereby ratifying and confirming all that said
  attorneys-in-fact as agents or any of them, or their substitute or substitutes,
  may lawfully do or cause to be done by virtue hereof.
  
         Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the dates indicated.
  
  <TABLE>
  <CAPTION>
  
                       SIGNATURE                                    TITLE                               DATE
  <S>                                                  <C>                                       <C>
  
          /s/ Ben M. Brigham                           President, Chief Executive                December 31, 1998
  ---------------------------------------------------- Officer and Chairman of  
              Ben M. Brigham                           the Board (principal     
                                                       executive officer)       
                                                       
  
          /s/ Anne L. Brigham                          Executive Vice President                  December 31, 1998
  ---------------------------------------------------- and Director
              Anne L. Brigham                   
  
  
          /s/ Jon L. Glass                             Vice President -                          December 31, 1998
  ---------------------------------------------------- Exploration and Director
              Jon L. Glass                     
  
  
          /s/ Craig M. Fleming                         Chief Financial Officer                   December 31, 1998
  ---------------------------------------------------- (principal financial and
              Craig M. Fleming                         accounting officer)
                                                       
  </TABLE>
  
  
  
                                        II-4
  
  <PAGE>   7
  
  
  <TABLE>
  <CAPTION>
  
                       SIGNATURE                                    TITLE                               DATE
  <S>                                                  <C>                                       <C>
  
                  /s/ Harold D. Carter                 Director                                  December 31, 1998
  -----------------------------------------------------
                    Harold D. Carter
  
  
                 /s/ Alexis M. Cranberg                Director                                  December 31, 1998
  ----------------------------------------------------
                   Alexis M. Cranberg
  
  
                 /s/  W. Craig Childers                Director                                  December 31, 1998
  ----------------------------------------------------
                    W. Craig Childers
  
  
                 /s/ Stephen P. Reynolds               Director                                  December 31, 1998
  -----------------------------------------------------
                   Stephen P. Reynolds
  </TABLE>
  
  
  
                                        II-5
  
  <PAGE>   8
  
  
  
                                  INDEX TO EXHIBITS
  <TABLE>
  <CAPTION>
  
  Exhibit Number                       Exhibit
  --------------                       -------
  <S>                  <C>
  
         4.1           Brigham, Inc. 401(k) Plan.
  
         5.1           Opinion of Thompson & Knight, A Professional Corporation.
  
         23.1          Consent of Thompson & Knight, A Professional Corporation
                       (included in the opinion of Thompson & Knight, P.C. filed
                       herewith as Exhibit 5.1).
  
         23.2          Consent of PricewaterhouseCoopers LLP.
  
         24.1          Power of Attorney (included on signature page of this
                       Registration Statement).
  </TABLE>
  
  
  
  
  
  
                                        II-6
metadata_documents: [{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 23634}]
metadata_filer: {"company-data": {"conformed-name": "BRIGHAM EXPLORATION CO", "cik": "0001034755", "assigned-sic": "1311", "irs-number": "752692967", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-70137", "film-number": "99500998"}, "business-address": {"street1": "6300 BRIDGE POINT PARKWAY", "street2": "BUILDING TWO, SUITE 500", "city": "AUSTIN", "state": "TX", "zip": "78730", "phone": "512-427-3300"}, "mail-address": {"street1": "6300 BRIDGE POINT PARKWAY", "street2": "BUILDING TWO, SUITE 500", "city": "AUSTIN", "state": "TX", "zip": "78730"}}
text: 1
       As filed with the Securities and Exchange Commission on January 5, 1999
                                              Registration Statement No. 333-
  ================================================================================
  
                         SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                                  ---------------
  
                                      FORM S-8
                               REGISTRATION STATEMENT
                                        UNDER
                             THE SECURITIES ACT OF 1933
  
                                  ---------------
  
                             BRIGHAM EXPLORATION COMPANY
               (Exact name of registrant as specified in its charter)
  
                       DELAWARE                           75-2692967
            (State or other jurisdiction      (I.R.S. Employer Identification No.)
          of incorporation or organization)         
  
   
  
  6300 BRIDGE POINT PARKWAY, BUILDING 2, SUITE 500
                    AUSTIN, TEXAS
      (Address of principal executive offices)
  
                        78730
                      (Zip Code)
  
                                    -------------
  
                                    BRIGHAM, INC.
                                     401(k) PLAN
              (AS AMENDED AND RESTATED EFFECTIVE AS OF JANUARY 1, 1999)
                              (Full title of the Plan)
  
                                    -------------
  
                                   Ben. M. Brigham
                         President, Chief Executive Officer
                              and Chairman of the Board
                             Brigham Exploration Company
                  6300 Bridge Point Parkway, Building 2, Suite 500
                                 Austin, Texas 78730
                                   (512) 427-3300
              (Name, address and telephone number of agent for service)
  
                                      Copy to:
                                   Joe Dannenmaier
                               Thompson & Knight, P.C.
                           1700 Pacific Avenue, Suite 3300
                                 Dallas, Texas 75201
                                   (214) 969-1700
  
                                    -------------
                           CALCULATION OF REGISTRATION FEE
  ====================================================================================================================================
              Title of securities to be          Amount to be    Proposed maximum offering    Proposed maximum           Amount of
                     registered                   registered        price per share(1)    aggregate offering price(1) registration fee
  ------------------------------------------------------------------------------------------------------------------------------------
  Common Stock, par value $.01 per share .... 300,000 shares (2)          $4.88                 $1,464,000                $407
  ------------------------------------------------------------------------------------------------------------------------------------
  Interests in the 401(k) Plan of            
  Brigham, Inc. .............................         (3)                   (4)                     (4)                    (4)
  ====================================================================================================================================
  (1)      Estimated solely for the purpose of calculating the registration fee
           pursuant to Rule 457(h) under the Securities Act of 1933 (the
           "Securities Act") and based on the average of the high and low prices
           of the common stock reported on The Nasdaq Stock Markets' National
           Market on December 30, 1998.
  (2)      If, as a result of stock splits, stock dividends or similar
           transactions, the number of securities purported to be registered on
           this Registration Statement changes, the provisions of Rule 416 shall
           apply to this Registration Statement, and this Registration Statement
           shall be deemed to cover the additional securities resulting from the
           split of, or the dividend on, the securities covered by this
           Registration Statement.
  (3)      Pursuant to Rule 416(c) under the Securities Act, this Registration
           Statement also covers an indeterminate amount of plan interests to be
           offered or sold pursuant to the Brigham Inc. 401(k) Plan.
  (4)      Pursuant to Rule 457(h)(2) under the Securities Act, no separate fee is
           required to register plan interests.
  
  ================================================================================
  2
  
                                       PART I
  
                INFORMATION REQUIRED IN THE SECTION 10(a) PROSPECTUS
  
  Item 1.      Plan Information.*
  
  Item 2.      Registrant Information and Employee Plan Annual Information.*
  
  -------------
  
  *        Information required by Part I to be contained in the Section 10(a)
           prospectus is omitted from this Registration Statement in accordance
           with Rule 428 under the Securities Act of 1933 and the Note to Part I
           of Form S-8.
  3
  
                                       PART II
  
                 INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
  
  Item 3.      Incorporation of Documents by Reference.
  
         The following documents have been filed by the Registrant with the
  Securities and Exchange Commission and are incorporated by reference in this
  Registration Statement:
  
         (1)    The Company's Annual Report on Form 10-K for the fiscal year ended
                December 31, 1997;
  
         (2)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                September 30, 1998;
  
         (3)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                June 30, 1998;
  
         (4)    The Company's Quarterly Report on Form 10-Q for the quarter ended
                March 31, 1998;
  
         (4)    The Company's Current Report on Form 8-K (Date of Event: November
                12, 1997) filed January 23, 1998;
  
         (5)    The description of the Company's Common Stock, $.01 par value per
                share, contained in the Registration Statement on Form 8-A
                (Registration No. 000-22433) of the Company heretofore filed with
                the Commission, including any amendments or reports filed for the
                purpose of updating such description.
  
         In addition, all documents filed by the Registrant pursuant to Sections
  13(a), 13(c), 14 and 15(d) of the Securities Exchange Act of 1934 subsequent to
  the date of this Registration Statement and prior to the filing of a
  post-effective amendment which indicates that all securities offered have been
  sold or which deregisters all securities then remaining unsold shall be deemed
  to be incorporated by reference in this Registration Statement and to be a part
  hereof from the date of filing of such documents. Any statement contained in a
  document incorporated or deemed to be incorporated by reference herein shall be
  deemed to be modified or superseded for purposes of this Registration Statement
  to the extent that a statement contained herein or in any other subsequently
  filed document which also is or is deemed to be incorporated by reference herein
  modifies or supersedes such statement. Any statement so modified or superseded
  shall not be deemed, except as so modified or superseded, to constitute a part
  of this Registration Statement. Upon the written or oral request of any person
  to whom a copy of this Registration Statement has been delivered, the Company
  will provide without charge to such person a copy of any and all documents
  (excluding exhibits thereto unless such exhibits are specifically incorporated
  by reference into such documents) that have been incorporated by reference into
  this Registration Statement but not delivered herewith. Requests for such
  documents should be addressed to Brigham Exploration Company, 6300 Bridge Point
  Parkway, Building 2, Suite 500, Austin, Texas 78730, Attention: Corporate
  Secretary, (512) 427-3300.
  
  Item 4.      Description of Securities.
  
         Not Applicable.
  
  Item 5.      Interests of Named Experts and Counsel.
  
         Not Applicable.
  
  Item 6.      Indemnification of Directors and Officers.
  
         In accordance with Section 102(b)(7) of the Delaware General Corporation
  Law ("DGCL") the Registrant's Certificate of Incorporation includes a provision
  that, to the fullest extent permitted by law, eliminates the personal liability
  of members of its board of directors to the corporation or its stockholders for
  monetary damages for breach of fiduciary duty as a director. Such provision does
  not eliminate or limit the liability of a director (1) for any breach of a
  director's duty of loyalty to the corporation or its stockholders, (2) for acts
  or omissions not in good faith or which involve intentional misconduct or a
  
                                        II-1
  4
  
  knowing violation of a law, (3) for paying an unlawful dividend or approving an
  illegal stock repurchase (as provided in Section 174 of the DGCL), or (4) for
  any transaction from which the director derived an improper personal benefit.
  
         Under Section 145 of the DGCL, the Registrant has the power to indemnify
  any person who was or is a party or is threatened to be made a party to any
  threatened, pending or completed action, suit or proceeding (other than an
  action by or in the right of the corporation) by reason of the fact that the
  person is or was a director, officer, employee or agent of any corporation,
  partnership, joint venture, trust or other enterprise, against any and all
  expenses (including attorneys' fees), judgments, fines and amounts paid in
  settlement and reasonably incurred in connection with such action, suit or
  proceeding. The power to indemnify applies only if the person acted in good
  faith and in a manner he reasonably believed to be in or not opposed to the best
  interests of the corporation, and with respect to any criminal action or
  proceeding, had no reasonable cause to believe the person's conduct was
  unlawful.
  
         In the case of an action by or in the right of the Registrant, no
  indemnification may be made with respect to any claim, issue or matter as to
  which such person shall have been adjudged to be liable to the corporation
  unless and only to the extent that the court of chancery or the court in which
  such action or suit was brought shall determine that despite the adjudication of
  liability such person is fairly and reasonably entitled to indemnity for such
  expenses which the court shall deem proper. Section 145 of the DGCL further
  provides that to the extent a director or officer of the Registrant has been
  successful in the defense of any action, suit or proceeding referred to above or
  in the defense of any claim, issue or matter therein, he shall be indemnified
  against expenses (including attorney's fees) actually and reasonably incurred by
  him in connection therewith.
  
         The Registrant also has the power to purchase and maintain insurance on
  behalf of any person covering any liability incurred by such person in his
  capacity as a director, officer, employee or agent of the corporation, or
  arising out of his status as such, whether or not the corporation would have the
  power to indemnify him against such liability.
  
         The Certificate of Incorporation and Bylaws provide that the Registrant
  will indemnify its officers and directors and former officers and directors
  against any expenses, judgments or settlement payments sustained or paid by such
  persons as a result of having acted as an officer or director of the Registrant,
  or, at the request of the Registrant, as an officer, director, agent or employee
  of another business entity. The Certificate of Incorporation and Bylaws further
  provide that the Registrant may, by action of its Board of Directors, provide
  indemnification to employees and agents of the Registrant, individually or as a
  group, with the same scope and effect as the indemnification of directors and
  officers.
  
         The Registrant has entered into an Indemnity Agreement with each of its
  executive officers which provides for the indemnification in certain instances
  against liability and expenses incurred in connection with proceedings brought
  by or in the right of the Registrant or by third parties by reason of the person
  serving as an officer or direction of the Registrant.
  
  Item 7.      Exemption from Registration Claimed.
  
         Not Applicable.
  
  Item 8.      Exhibits.
  
         The following documents are filed as exhibits to this Registration
  Statement:
  
                4.1   Brigham, Inc. 401(k) Plan.
  
                5.1   Opinion of Thompson & Knight, A Professional Corporation.
  
                23.1  Consent of Thompson & Knight, A Professional Corporation
                      (included in the opinion of Thompson & Knight, P.C. filed
                      herewith as Exhibit 5.1).
  
                23.2  Consent of PricewaterhouseCoopers LLP.
  
                24.1  Power of Attorney (included on signature page of this
                      Registration Statement).
  
                                        II-2
  5
  
  Item 9.      Undertakings.
  
         The Registrant hereby undertakes:
  
               (1) To file, during any period in which offers or sales are being
         made, a post-effective amendment to this Registration Statement:
  
                   (i) To include any prospectus required by Section 10(a)(3) of
               the Securities Act of 1933;
  
                   (ii) To reflect in the prospectus any facts or events arising
               after the effective date of this Registration Statement (or the
               most recent post-effective amendment thereof) which, individually
               or in the aggregate, represent a fundamental change in the
               information set forth in this Registration Statement.
               Notwithstanding the foregoing, any increase or decrease in volume
               of securities offered (if the total dollar value of securities
               offered would not exceed that which was registered) and any
               deviation from the low or high end of the estimated maximum
               offering range may be reflected in the Form of prospectus filed
               with the Commission pursuant to Rule 424(b) if, in the aggregate,
               the changes in volume and price represent no more than a 20% change
               in the maximum aggregate offering price set forth in the
               "Calculation of Registration Fee" table in the effective
               registration statement; and
  
                   (iii) To include any material information with respect to the
               plan of distribution not previously disclosed in this Registration
               Statement or any material change to such information in this
               Registration Statement;
  
         provided, however, that paragraphs (1)(i) and (1)(ii) do not apply if the
         information required to be included in a post-effective amendment by
         those paragraphs is contained in periodic reports filed by the Registrant
         pursuant to Section 13 or Section 15(d) of the Securities Exchange Act of
         1934 that are incorporated by reference in this Registration Statement.
  
               (2) That, for the purpose of determining any liability under the
         Securities Act of 1933, each such post-effective amendment shall be
         deemed to be a new registration statement relating to the securities
         offered therein, and the offering of such securities at that time shall
         be deemed to be the initial bona fide offering thereof.
  
               (3) To remove from registration by means of a post-effective
         amendment any of the securities being registered which remain unsold at
         the termination of the offering.
  
               (4) That, for purposes of determining any liability under the
         Securities Act of 1933, each filing of the Registrant's annual report
         pursuant to Section 13(a) or Section 15(d) of the Securities Exchange Act
         of 1934 that is incorporated by reference in this Registration Statement
         shall be deemed to be a new registration statement relating to the
         securities offered therein, and the offering of such securities at that
         time shall be deemed to be the initial bona fide offering thereof.
  
               (5) Insofar as indemnification for liabilities arising under the
         Securities Act of 1933 may be permitted to directors, officers and
         controlling persons of the Registrant pursuant to the foregoing
         provisions, or otherwise, the Registrant has been advised that in the
         opinion of the Securities and Exchange Commission such indemnification is
         against public policy as expressed in the Act and is, therefore,
         unenforceable. In the event that a claim for indemnification against such
         liabilities (other than the payment by the Registrant of expenses
         incurred or paid by a director, officer or controlling person of the
         Registrant in the successful defense of any action, suit or proceeding)
         is asserted by such director, officer or controlling person in connection
         with the securities being registered, the Registrant will, unless in the
         opinion of its counsel the matter has been settled by controlling
         precedent, submit to a court of appropriate jurisdiction the question
         whether such indemnification by it is against public policy as expressed
         in the Act and will be governed by the final adjudication of such issue.
  
                                        II-3
  6
  
                                     SIGNATURES
  
         Pursuant to the requirements of the Securities Act of 1933, the
  Registrant certifies that it has reasonable grounds to believe that it meets all
  of the requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in the City of Austin and State of Texas on the 31 day of December,
  1998.
  
                                     BRIGHAM EXPLORATION COMPANY
  
                                     By:   /s/ Ben M. Brigham
                                           -------------------------------------
                                           Ben M. Brigham, President, 
                                           Chief Executive Officer
                                           and Chairman of the Board
  
                                  POWER OF ATTORNEY
  
         KNOW ALL MEN BY THESE PRESENTS, that the undersigned directors and
  officers of Brigham Exploration Company, a Delaware corporation, which is filing
  a Registration Statement on Form S-8 with the Securities and Exchange Commission
  under the provisions of the Securities Act of 1933, as amended, hereby
  constitute and appoint Ben M. Brigham and Anne L. Brigham, and each of them, his
  true and lawful attorneys-in-fact and agents, with full power of substitution
  and resubstitution, for him and in his name, place and stead, in any and all
  capacities, to sign such Registration Statement and any or all amendments to the
  Registration Statement, and all other documents in connection therewith to be
  filed with the Securities and Exchange Commission, granting unto said
  attorneys-in-fact and agents, and each of them, full power and authority to do
  and perform each and every act and thing requisite and necessary to be done in
  and about the premises, as fully to all intents and purposes as he might or
  could do in person, hereby ratifying and confirming all that said
  attorneys-in-fact as agents or any of them, or their substitute or substitutes,
  may lawfully do or cause to be done by virtue hereof.
  
         Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the dates indicated.
  SIGNATURE                                    TITLE                               DATE
  /s/ Ben M. Brigham                           President, Chief Executive                December 31, 1998
  ---------------------------------------------------- Officer and Chairman of  
              Ben M. Brigham                           the Board (principal     
                                                       executive officer)       
                                                       
  
          /s/ Anne L. Brigham                          Executive Vice President                  December 31, 1998
  ---------------------------------------------------- and Director
              Anne L. Brigham                   
  
          /s/ Jon L. Glass                             Vice President -                          December 31, 1998
  ---------------------------------------------------- Exploration and Director
              Jon L. Glass                     
  
          /s/ Craig M. Fleming                         Chief Financial Officer                   December 31, 1998
  ---------------------------------------------------- (principal financial and
              Craig M. Fleming                         accounting officer)
  II-4
  7
  SIGNATURE                                    TITLE                               DATE
  /s/ Harold D. Carter                 Director                                  December 31, 1998
  -----------------------------------------------------
                    Harold D. Carter
  
                 /s/ Alexis M. Cranberg                Director                                  December 31, 1998
  ----------------------------------------------------
                   Alexis M. Cranberg
  
                 /s/  W. Craig Childers                Director                                  December 31, 1998
  ----------------------------------------------------
                    W. Craig Childers
  
                 /s/ Stephen P. Reynolds               Director                                  December 31, 1998
  -----------------------------------------------------
                   Stephen P. Reynolds
  II-5
  8
  
                                  INDEX TO EXHIBITS
  Exhibit Number                       Exhibit
  --------------                       -------
  4.1           Brigham, Inc. 401(k) Plan.
  
         5.1           Opinion of Thompson & Knight, A Professional Corporation.
  
         23.1          Consent of Thompson & Knight, A Professional Corporation
                       (included in the opinion of Thompson & Knight, P.C. filed
                       herewith as Exhibit 5.1).
  
         23.2          Consent of PricewaterhouseCoopers LLP.
  
         24.1          Power of Attorney (included on signature page of this
                       Registration Statement).
  II-6