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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000040730</issuerCik>
        <issuerName>GENERAL MOTORS CORP</issuerName>
        <issuerTradingSymbol>GM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001174451</rptOwnerCik>
            <rptOwnerName>KATEN KAREN L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 RENAISSANCE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>MC: 482-C38-B71</rptOwnerStreet2>
            <rptOwnerCity>DETROIT</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>482653000</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2004-08-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>41.82</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>75.50</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2001-01-10</value>
            </exerciseDate>
            <expirationDate>
                <value>2010-01-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2311</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2311</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>52.35</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2002-01-08</value>
            </exerciseDate>
            <expirationDate>
                <value>2011-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2830</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2830</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>50.46</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2003-01-07</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-01-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>GM Stock $1-2/3 Par Value, Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1988-08-08</value>
            </exerciseDate>
            <expirationDate>
                <value>1988-08-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>13472</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13472</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Director stock options granted pursuant to Section 16b-3 qualified General Motors Compensation Plan for Non-Employee Directors.</footnote>
        <footnote id="F2">Director stock option granted pursuant to Section 16b-3 qualified  General Motors Compensation Plan for Non-Employee Directors. The stock option vests in 3 equal annual installments, with the first installment exercisable on the date indicated.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Martin I. Darvick - Attorney-in-Fact for</signatureName>
        <signatureDate>2004-08-17</signatureDate>
    </ownerSignature>
</ownershipDocument>

