<?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>0001180585</rptOwnerCik><rptOwnerName>BRYAN JOHN H</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>300 RENAISSANCE CENTER P.O. BOX 300</rptOwnerStreet1><rptOwnerStreet2>MAIL CODE: 482-C38-B71</rptOwnerStreet2><rptOwnerCity>DETROIT</rptOwnerCity><rptOwnerState>MI</rptOwnerState><rptOwnerZipCode>48265-3000</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></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" 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Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>1202.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1202.0000</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="F3" /></securityTitle><conversionOrExercisePrice><value>71.5300</value></conversionOrExercisePrice><exerciseDate><value>2000-01-11</value></exerciseDate><expirationDate><value>2009-01-12</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par 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Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>2311.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2311.0000</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="F3" /></securityTitle><conversionOrExercisePrice><value>52.3500</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>2830.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2830.0000</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="F3" /></securityTitle><conversionOrExercisePrice><value>50.4600</value></conversionOrExercisePrice><exerciseDate><value>2003-01-07</value><footnoteId id="F8" /></exerciseDate><expirationDate><value>2012-01-08</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>3000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>3000.0000</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">Director stock options granted pursuant to Section 16b-3 qualified General Motors Corporation Deferred Compensation Plan for Non-Employee Directors.</footnote><footnote id="F4">In connection with the Hughes Transactions, the reporting person agreed to cancel these GM Class H Common Stock Options in exchange for 180 GM $1-2/3 par value common stock Restricted Stock Units having equivalent economic value.</footnote><footnote id="F5">Restricted Stock Units credited pursuant to Rule 16b-3 qualified GM Compensation Plan for Non-Employee Directors.  Deferred compensation, equal to the retainers earned during the year, is credited annually on each December 31.  The deferred compensation is converted into Restricted Stock Units at the average daily closing market price of GM Common Stock for such year.  The amounts credited during the year also include dividend equivalents on such Restricted Stock Units.  Pursuant to such Plan, the Restricted Stock Units are deferred until after the director's retirement from GM and are paid in cash.  The Restricted Stock Units convert on a one for one basis.  </footnote><footnote id="F6">In connection with the Hughes Transactions, the reporting person agreed to cancel 3,733 GM Class H common stock Restricted Stock Units in exchange for 1,171 GM $1-2/3 par value Restricted Stock Units having equivalent economic value.</footnote><footnote id="F7">Includes 1,171 GM $1-2/3 par value Restricted Stock Units received from the exchange of GM Class H common stock Restricted Stock Units and 180 GM $1-2/3 par value Restricted Stock Units received from the exchange of GM Class H common stock options.</footnote><footnote id="F8">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: /s/ Martin I. Darvick - Attorney-in-Fact for John H. Bryan</signatureName><signatureDate>2003-12-23</signatureDate></ownerSignature></ownershipDocument>

