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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-06-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181688</rptOwnerCik>
            <rptOwnerName>DEVINE JOHN M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 RENAISSANCE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>M/C: 482-C39-B30</rptOwnerStreet2>
            <rptOwnerCity>DETROIT</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>482653000</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Chairman &amp; CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6627</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.27</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>172972</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>476</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>GM Phantom Stock Units $1-2/3 Par Value Com Stock</value>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2178</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2178</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="F5"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>52.54</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2001-12-13</value>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2010-12-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>500000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>500000</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="F6"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>52.35</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2002-01-08</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2011-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>200000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>200000</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="F6"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>50.46</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2003-01-07</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-01-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>200000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>200000</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="F6"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>50.82</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2003-02-04</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-02-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</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="F6"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>40.05</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2004-01-21</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-01-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>200000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>200000</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="F6"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>53.92</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2005-01-23</value>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2014-01-24</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>160000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>160000</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, Deferred Stock Units</value>
                <footnoteId id="F7"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>52250</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52250</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</value>
                <footnoteId id="F8"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F8"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>75000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>75000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Devine transferred his right to receive 6,627 Restricted Stock Units orginally to be delivered on 12/31/2004, valued at the average market price on the date of transfer, to GM as reimbursement for GM's inadvertent excess withholding tax  paid on Mr. Devine's behalf to the government for 2003.  Promptly upon discovery of this inadvertent error, GM informed Mr. Devine and Mr. Devine executed this transaction, which transferred to GM an asset of equivalent value.</footnote>
        <footnote id="F2">Includes 12,413 Restricted Stock Units to be delivered on 12/31/2004, 19,040 Restricted Stock Units to be delivered on 12/31/2005 and 95,200 Restricted Stock Units to be delivered 18 months after my retirement.  Restricted Stock Units are payable in stock and are subject to forfeiture.  Dividend equivalents are earned on the Restricted Stock Units until shares are delivered.</footnote>
        <footnote id="F3">Shares held in trust under General Motors Stock Purchase Program as of 12/31/03.  State Street Bank &amp; Trust Co., Trustee.  Shares owned pursuant to Rule 16b-3 exempt employee savings plan.</footnote>
        <footnote id="F4">The Phantom Stock Units are held under Section 16b-3(c) exempt Rule 16b-3(b)(2) eligible excess benefit plan operated in conjunction with a qualified 401(k) plan.  The Units are payable in cash upon separation from General Motors.  These Units are being reported even though they are exempt under Rule 16b-3.  Units held as of 12/31/03.  The price of zero is fictional and only used for purposes of facilitating the electronic filing of this Form.</footnote>
        <footnote id="F5">Employee stock options granted pursuant to Rule 16b-3 qualified General Motors Stock Incentive Plan; stock options are exercisable in five equal annual installments, commencing, respectively, one, two, three, four and five years from the date of initial grant.</footnote>
        <footnote id="F6">Employee stock option granted pursuant to Rule 16b-3 qualified General Motors Stock Incentive Plan.  Stock option is exercisable in three equal annual installments, commencing, respectively, one, two and three years from the date of initial grant.</footnote>
        <footnote id="F7">The Deferred Stock Units were accrued under the Rule 16b-3 qualified General Motors Deferred Compensation Plan.  Dividend equivalents are earned on each Deferred Stock Unit.  Units held as of 01/23/04.  The Deferred Stock Units convert on a '1 for 1' basis.</footnote>
        <footnote id="F8">The Restricted Stock Units were accrued under the Rule 16b-3 qualified General Motors Annual Incentive Plan.  Dividend equivalents are earned on each Restricted Stock Unit.  Units held as of 01/23/04.  The Restricted Stock Units convert on a '1 for 1' basis.  The price of zero is fictional and only used for purposes of facilitating the electronic filing of this Form.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Martin I. Darvick - Attorney-in-Fact for</signatureName>
        <signatureDate>2004-06-10</signatureDate>
    </ownerSignature>
</ownershipDocument>

