<?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>0001181687</rptOwnerCik><rptOwnerName>GOTTSCHALK THOMAS A</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>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Exec. VP and General Counsel</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>17541.0000</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><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>1887.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F2" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>Trust</value><footnoteId id="F3" /></natureOfOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>49812.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1992.0000</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 Stock $1-2/3 Par Value Option (Right to Buy)</value><footnoteId id="F4" /></securityTitle><conversionOrExercisePrice><value>40.0700</value></conversionOrExercisePrice><exerciseDate><value>1997-02-05</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2006-02-06</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>43151.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>43151.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>44.7300</value></conversionOrExercisePrice><exerciseDate><value>1998-02-03</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2007-02-04</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>62971.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>62971.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>46.5900</value></conversionOrExercisePrice><exerciseDate><value>1999-01-12</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2008-01-13</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>64680.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>64680.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>71.5300</value></conversionOrExercisePrice><exerciseDate><value>2000-01-11</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2009-01-12</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>71653.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>71653.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>75.5000</value></conversionOrExercisePrice><exerciseDate><value>2001-01-10</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2010-01-11</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>65000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>65000.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>52.3500</value></conversionOrExercisePrice><exerciseDate><value>2002-01-08</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2011-01-09</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>70000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>70000.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>50.4600</value></conversionOrExercisePrice><exerciseDate><value>2003-01-07</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2012-01-08</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>90000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>90000.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>50.8200</value></conversionOrExercisePrice><exerciseDate><value>2003-02-04</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2012-02-05</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>50000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>50000.0000</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="F4" /></securityTitle><conversionOrExercisePrice><value>40.0500</value></conversionOrExercisePrice><exerciseDate><value>2004-01-21</value><footnoteId id="F4" /></exerciseDate><expirationDate><value>2013-01-22</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>90000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>90000.0000</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="F5" /></securityTitle><conversionOrExercisePrice><footnoteId id="F5" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F5" /></exerciseDate><expirationDate><footnoteId id="F5" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>General Motors Common Stock, $1-2/3 Par Value</value></underlyingSecurityTitle><underlyingSecurityShares><value>40000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>40000.0000</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">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="F4">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="F5">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 Thomas A. Gottschalk</signatureName><signatureDate>2003-12-23</signatureDate></ownerSignature></ownershipDocument>

