<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-04-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000108601</issuerCik>
        <issuerName>WRIGLEY WM JR CO</issuerName>
        <issuerTradingSymbol>WWY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001087398</rptOwnerCik>
            <rptOwnerName>PRITZKER PENNY S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>PRITZKER REALTY GROUP, L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>200 W. MADISON STREET, SUITE 3700</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-04-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>266.41</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>59.12</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>266.41</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20813.21</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share unit is equivalent to one share of the Company's Common Stock.</footnote>
        <footnote id="F2">Acquired under the Non-Employee Director Deferred Compensation Plan (NEDDCP), which Plan is 16b-3 exempt.</footnote>
        <footnote id="F3">The equivalent value of share units acquired under the Deferred Compensation Plan for non-employee Directors may be transferred to other funds within the grantor trust for the Plan but may not be distributed until the earlier of age 70 or retirement from the Board.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: /s/ Mark Monroe under POA for Penny Pritzker</signatureName>
        <signatureDate>2004-04-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0201
4
2004-04-01
0
0000108601
WRIGLEY WM JR CO
WWY
0001087398
PRITZKER PENNY S
PRITZKER REALTY GROUP, L.P.
200 W. MADISON STREET, SUITE 3700
CHICAGO
IL
60606
1
0
0
0
Common Stock Units
0.00
2004-04-01
4
A
0
266.41
59.12
A
Common Stock
266.41
20813.21
D
Each share unit is equivalent to one share of the Company's Common Stock.
Acquired under the Non-Employee Director Deferred Compensation Plan (NEDDCP), which Plan is 16b-3 exempt.
The equivalent value of share units acquired under the Deferred Compensation Plan for non-employee Directors may be transferred to other funds within the grantor trust for the Plan but may not be distributed until the earlier of age 70 or retirement from the Board.
By: /s/ Mark Monroe under POA for Penny Pritzker
2004-04-02