<?xml version="1.0"?><ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-12-22</periodOfReport><notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000040730</issuerCik>
        <issuerName>GENERAL MOTORS CORP</issuerName>
        <issuerTradingSymbol>GM &amp; GMH</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181688</rptOwnerCik>
            <rptOwnerName>DEVINE JOHN M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>GENERAL MOTORS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>300 RENAISSANCE CENTER MC: 482-C39-B30</rptOwnerStreet2>
            <rptOwnerCity>DETROIT</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48265-3000</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>GM Class H Common Stock, $.10 Par Value</value></securityTitle><transactionDate><value>2003-12-22</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>D</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>3503.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F2" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>158882.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value><footnoteId id="F3" /></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>69.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>Trust</value><footnoteId id="F4" /></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F5" /></securityTitle><conversionOrExercisePrice><value>52.5400</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>500000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>500000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F6" /></securityTitle><conversionOrExercisePrice><value>52.3500</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>200000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>200000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F6" /></securityTitle><conversionOrExercisePrice><value>50.4600</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>200000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>200000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F6" /></securityTitle><conversionOrExercisePrice><value>50.8200</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>100000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>100000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F6" /></securityTitle><conversionOrExercisePrice><value>40.0500</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>200000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>200000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value, Deferred Stock Units</value><footnoteId id="F7" /></securityTitle><conversionOrExercisePrice><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>49589.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>49589.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>GM Stock $1-2/3 Par Value, Restricted Stock Units</value><footnoteId id="F8" /></securityTitle><conversionOrExercisePrice><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>75000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>75000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">The reported shares of GM Class H common stock were redeemed by GM in connection with a series of transactions pursuant to which Hughes Electronics Corporation was separated from GM and The News Corporation Limited acquired a 34% interest in Hughes (the 'Hughes Transactions'). Each share of GM Class H common stock held by the reporting person was redeemed by GM in exchange for one share of Hughes common stock. Immediately after such redemption, Hughes was merged with and into a subsidiary of News Corporation and a portion of the shares of Hughes common stock received by the reporting person in connection with the redemption was converted in the subsequent merger into News Corporation preferred American depositary shares.</footnote><footnote id="F2">As a result of the Hughes Transactions, the reporting person received in exchange for each share of GM Class H Common Stock (1) 0.82321617207 of a share of Hughes common stock and (2) 0.09207432110 of a News Corporation preferred American depositary share. The closing price for a share of Hughes common stock on December 23, 2003, the first day such shares were publicly traded, was $16.90, and the closing price of each News Corporation preferred American depositary share on December 22, 2003, the effective date of the Hughes Transactions, was $28.65.</footnote><footnote id="F3">Restricted Stock Unit grant, 19,040 shares to be delivered on each of 12/13/04 and 12/13/05. Also, 95,200 shares are to be delivered 18 months after the reporting person's retirement. Shares are subject to forfeiture. Dividend equivalents are earned on each share until delivered.</footnote><footnote id="F4">Shares held in trust under General Motors Stock Purchase Program as of 12/31/02. State Street Bank &amp; Trust Co., Trustee. Shares owned pursuant to Rule 16b-3 exempt employee savings plan.</footnote><footnote id="F5">Employee stock options granted pursuant to Section 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 Section 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 12/31/02. 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 1/21/03. The Restricted Stock Units convert on a '1 for 1' basis.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>By: /s/ Martin I. Darvick - Attorney-in-Fact for John M. Devine</signatureName><signatureDate>2003-12-23</signatureDate></ownerSignature></ownershipDocument>

