content: <PAGE>   1
        As filed with the Securities and Exchange Commission on June 16, 1998
                                              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                          78730
  (Address of principal executive offices)                (Zip Code)
  
                                -------------------
  
                                 1997 INCENTIVE PLAN
                           OF BRIGHAM EXPLORATION COMPANY
                              (Full title of the Plan)
  
                                -------------------
  
                    Ben M. Brigham                              Copy to:         
          Chief Executive Officer, President                 Joe Dannenmaier     
               and Chairman of the Board                   Thompson & Knight,    
              Brigham Exploration Company              A Professional Corporation
   6300 Bridge Point Parkway, Building 2, Suite 500        1700 Pacific Avenue   
                  Austin, Texas 78730                          Suite 3300        
        (Name and address of agent for service)            Dallas, Texas 75201   
                                                             (214) 969-1700      
                    (512) 427-3300                    
             (Telephone number, including
           area code, of agent for service)
  
                                -------------------
  
                           CALCULATION OF REGISTRATION FEE
  
  <TABLE>
  <CAPTION>
  ===============================================================================================================================
   Title of securities to be     Amount to be     Proposed maximum offering        Proposed maximum             Amount of
           registered           registered(1)         price per share(2)     aggregate offering price(2)     registration fee
  -------------------------------------------------------------------------------------------------------------------------------
  <S>                             <C>                       <C>                      <C>                          <C>   
  Common Stock par value          1,588,169                 $10.91                   $17,326,923                  $5,111
  $.01 per share .............      shares
  ===============================================================================================================================
  </TABLE>
  
  (1)  Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
       any stock split, stock dividend or similar transaction with respect to
       these shares are also being registered hereunder.
  
  (2)  Estimated solely for the purpose of determining the registration fee
       pursuant to Rule 457(h).
  
  
  
  ================================================================================
  <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 filed by the Registrant with the Securities and
  Exchange Commission are incorporated by reference in this Registration
  Statement:
  
         (1)    The Company's Quarterly Report on Form 10-Q for the fiscal quarter
                ended March 31, 1998.
  
         (2)    The Company's Annual Report on Form 10-K for the fiscal year ended
                December 31, 1997.
  
         (3)    The Company's Current Report on Form 8-K (Date of Event: November
                12, 1997) dated January 23, 1998.
  
         (4)    All other reports filed by the Company pursuant to Section 13(a)
                or 15(d) of the Exchange Act since December 31, 1997.
  
         (5)    The description of the Common Stock contained in the Company's
                Registration Statement on Form 8-A (Registration Statement No.
                000-22433), including any amendment or report 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.
  
  
  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 Company'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 Company 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 Company or its stockholders, (2) for acts or
  omissions not in good faith or which involve intentional misconduct or a 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, reasonably incurred in
  connection with such action,
  
  
  
  
                                        II-1
  
  <PAGE>   4
  
  
  
  
  suit or proceeding. The power to indemnify applies only if the person acted in
  good faith and in a manner the person 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 Registrant 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, that person shall be
  indemnified against expenses (including attorney's fees) actually and reasonably
  incurred in connection therewith.
  
         The Registrant also has the power to purchase and maintain insurance on
  behalf of any person covering any liability incurred in that person's capacity
  as a director, officer, employee or agent of the corporation, or arising out of
  that person's status as such, whether or not the corporation would have the
  power to indemnify against the 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 Company 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 Company or by third parties by reason of a person
  serving as an officer or director of the Company.
  
  Item 7.      Exemption from Registration Claimed.
  
         Not Applicable.
  
  
  Item 8.      Exhibits.
  
         The following documents are filed as exhibits to this Registration
  Statement:
  
         4.1    1997 Incentive Plan of Brigham Exploration Company (filed as
                Exhibit 10.9 to the Registrant's Registration Statement on Form
                S-1 (Registration No. 333-22491)) and incorporated herein by
                reference.
  
         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 Price Waterhouse 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 28th day of May,
  1998.
  
                                            BRIGHAM EXPLORATION COMPANY
  
  
                                            By:   /s/ Ben M. Brigham
                                                  -------------------------------
                                                  Ben M. Brigham, Chief Executive
                                                  Officer, President 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                   Chief Executive Officer,                     May 28, 1998
  --------------------------------------       President and Chairman of 
             Ben M. Brigham                    the Board (principal      
                                               executive officer)        
                                               
  
         /s/ Anne L. Brigham                   Executive Vice President                     May 28, 1998
  --------------------------------------       and Director
            Anne L. Brigham                    
  
  
          /s/ Jon L. Glass                     Vice President -                             May 28, 1998
  --------------------------------------       Exploration and Director
            Jon L. Glass                       
  
  
          /s/ Craig M. Fleming                 Chief Financial Officer                      May 28, 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          May 28, 1998
  --------------------------------------
          Harold D. Carter
  
  
       /s/ Alexis M. Cranberg                Director          May 28, 1998
  --------------------------------------
         Alexis M. Cranberg
  
  
        /s/ Gary J. Milavec                  Director          May 28, 1998
  --------------------------------------
          Gary J. Milavec
  
  
      /s/ Stephen P. Reynolds                Director          May 28, 1998
  --------------------------------------
         Stephen P. Reynolds
  </TABLE>
  
  
  
  
  
                                        II-5
  
  <PAGE>   8
  
  
  
  
                                  INDEX TO EXHIBITS
  
  <TABLE>
  <CAPTION>
  Exhibit Number               Exhibit
  --------------               -------
  <S>           <C>
      4.1       1997 Incentive Plan of Brigham Exploration Company (filed as
                Exhibit 10.9 to the Registrant's Registration Statement on Form
                S-1 (Registration Statement No. 333-22491)) and incorporated
                herein by reference.
  
      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 Price Waterhouse LLP.
  
     24.1       Power of Attorney (included on signature page of this Registration
                Statement).
  </TABLE>
metadata_documents: [{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 20983}]
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": "333-56961", "film-number": "98649219"}, "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 June 16, 1998
                                              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                          78730
  (Address of principal executive offices)                (Zip Code)
  
                                -------------------
  
                                 1997 INCENTIVE PLAN
                           OF BRIGHAM EXPLORATION COMPANY
                              (Full title of the Plan)
  
                                -------------------
  
                    Ben M. Brigham                              Copy to:         
          Chief Executive Officer, President                 Joe Dannenmaier     
               and Chairman of the Board                   Thompson & Knight,    
              Brigham Exploration Company              A Professional Corporation
   6300 Bridge Point Parkway, Building 2, Suite 500        1700 Pacific Avenue   
                  Austin, Texas 78730                          Suite 3300        
        (Name and address of agent for service)            Dallas, Texas 75201   
                                                             (214) 969-1700      
                    (512) 427-3300                    
             (Telephone number, including
           area code, of agent for service)
  
                                -------------------
  
                           CALCULATION OF REGISTRATION FEE
  ===============================================================================================================================
   Title of securities to be     Amount to be     Proposed maximum offering        Proposed maximum             Amount of
           registered           registered(1)         price per share(2)     aggregate offering price(2)     registration fee
  -------------------------------------------------------------------------------------------------------------------------------
  Common Stock par value          1,588,169                 $10.91                   $17,326,923                  $5,111
  $.01 per share .............      shares
  ===============================================================================================================================
  (1)  Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
       any stock split, stock dividend or similar transaction with respect to
       these shares are also being registered hereunder.
  
  (2)  Estimated solely for the purpose of determining the registration fee
       pursuant to Rule 457(h).
  
  ================================================================================
  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 filed by the Registrant with the Securities and
  Exchange Commission are incorporated by reference in this Registration
  Statement:
  
         (1)    The Company's Quarterly Report on Form 10-Q for the fiscal quarter
                ended March 31, 1998.
  
         (2)    The Company's Annual Report on Form 10-K for the fiscal year ended
                December 31, 1997.
  
         (3)    The Company's Current Report on Form 8-K (Date of Event: November
                12, 1997) dated January 23, 1998.
  
         (4)    All other reports filed by the Company pursuant to Section 13(a)
                or 15(d) of the Exchange Act since December 31, 1997.
  
         (5)    The description of the Common Stock contained in the Company's
                Registration Statement on Form 8-A (Registration Statement No.
                000-22433), including any amendment or report 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.
  
  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 Company'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 Company 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 Company or its stockholders, (2) for acts or
  omissions not in good faith or which involve intentional misconduct or a 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, reasonably incurred in
  connection with such action,
  
                                        II-1
  4
  
  suit or proceeding. The power to indemnify applies only if the person acted in
  good faith and in a manner the person 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 Registrant 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, that person shall be
  indemnified against expenses (including attorney's fees) actually and reasonably
  incurred in connection therewith.
  
         The Registrant also has the power to purchase and maintain insurance on
  behalf of any person covering any liability incurred in that person's capacity
  as a director, officer, employee or agent of the corporation, or arising out of
  that person's status as such, whether or not the corporation would have the
  power to indemnify against the 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 Company 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 Company or by third parties by reason of a person
  serving as an officer or director of the Company.
  
  Item 7.      Exemption from Registration Claimed.
  
         Not Applicable.
  
  Item 8.      Exhibits.
  
         The following documents are filed as exhibits to this Registration
  Statement:
  
         4.1    1997 Incentive Plan of Brigham Exploration Company (filed as
                Exhibit 10.9 to the Registrant's Registration Statement on Form
                S-1 (Registration No. 333-22491)) and incorporated herein by
                reference.
  
         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 Price Waterhouse 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 28th day of May,
  1998.
  
                                            BRIGHAM EXPLORATION COMPANY
  
                                            By:   /s/ Ben M. Brigham
                                                  -------------------------------
                                                  Ben M. Brigham, Chief Executive
                                                  Officer, President 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                   Chief Executive Officer,                     May 28, 1998
  --------------------------------------       President and Chairman of 
             Ben M. Brigham                    the Board (principal      
                                               executive officer)        
                                               
  
         /s/ Anne L. Brigham                   Executive Vice President                     May 28, 1998
  --------------------------------------       and Director
            Anne L. Brigham                    
  
          /s/ Jon L. Glass                     Vice President -                             May 28, 1998
  --------------------------------------       Exploration and Director
            Jon L. Glass                       
  
          /s/ Craig M. Fleming                 Chief Financial Officer                      May 28, 1998
  --------------------------------------       (principal financial and
            Craig M. Fleming                   accounting officer)
  II-4
  7
  SIGNATURE                         TITLE               DATE
             ---------                         -----               ----
  /s/ Harold D. Carter                 Director          May 28, 1998
  --------------------------------------
          Harold D. Carter
  
       /s/ Alexis M. Cranberg                Director          May 28, 1998
  --------------------------------------
         Alexis M. Cranberg
  
        /s/ Gary J. Milavec                  Director          May 28, 1998
  --------------------------------------
          Gary J. Milavec
  
      /s/ Stephen P. Reynolds                Director          May 28, 1998
  --------------------------------------
         Stephen P. Reynolds
  II-5
  8
  
                                  INDEX TO EXHIBITS
  Exhibit Number               Exhibit
  --------------               -------
  4.1       1997 Incentive Plan of Brigham Exploration Company (filed as
                Exhibit 10.9 to the Registrant's Registration Statement on Form
                S-1 (Registration Statement No. 333-22491)) and incorporated
                herein by reference.
  
      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 Price Waterhouse LLP.
  
     24.1       Power of Attorney (included on signature page of this Registration
                Statement).