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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-01-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181765</rptOwnerCik>
            <rptOwnerName>STEPHENS THOMAS G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>777 JOSLIN AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PONTIAC</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>483402925</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Group Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2005-01-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10025</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.17</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25168</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2005-01-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8454</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.33</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16714</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>General Motors Common Stock, $1-2/3 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2005-01-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>578</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.33</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16136</value>
                </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>470</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Trust</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>GM Stock $1-2/3 Par Value Option (Right To Buy)</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>33.17</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-01-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10025</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.17</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>1996-01-09</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2005-01-10</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10025</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>GM Phantom Stock Units $1-2/3 Par Value Com Stock</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2336</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2336</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>40.07</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1997-02-05</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2006-02-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15648</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15648</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>44.73</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1998-02-03</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2007-02-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>18257</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18257</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>46.59</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1999-01-12</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2008-01-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>18030</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18030</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>71.53</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2000-01-11</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2009-01-12</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20434</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20434</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>75.50</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2001-01-10</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2010-01-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>18000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18000</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>52.35</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2002-01-08</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2011-01-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20000</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>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>40000</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>50.82</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2003-02-04</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-02-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20000</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>40.05</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2004-01-21</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-01-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>40000</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>53.92</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2005-01-23</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2014-01-24</value>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>General Motors Common Stock, $1-2/3 Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>32000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>32000</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="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>39813</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39813</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">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="F2">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.  Date shown is the date the first installment is/was exercisable.</footnote>
        <footnote id="F3">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="F4">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.  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>2005-01-10</signatureDate>
    </ownerSignature>
</ownershipDocument>

