<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-05</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000711039</issuerCik><issuerName>MAXTOR CORP</issuerName>        <issuerTradingSymbol>MXO</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001201521</rptOwnerCik><rptOwnerName>WINGERT MICHAEL J</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>500 MCCARTHY BLVD.</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>MILPITAS</rptOwnerCity><rptOwnerState>CA</rptOwnerState><rptOwnerZipCode>95035</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Exec. VP, GM Server Products</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>12500</value></transactionShares><transactionPricePerShare><value>4.91</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>12500</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>12500</value></transactionShares><transactionPricePerShare><value>10</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Employee Stock Option (right to buy)</value></securityTitle><conversionOrExercisePrice><value>4.91</value></conversionOrExercisePrice><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>12500</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2002-10-31</value><footnoteId id="F1" /></exerciseDate><expirationDate><value>2011-10-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>12500</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>302187</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Grant of options pursuant to Issuer's stock option plan, vesting over four years at the rate of 25% on the first anniversary of the grant date, as listed in the table, and at the rate of 6.25% quarterly thereafter.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Glenn H. Stevens by power-of-attorney.</signatureName><signatureDate>2003-08-07</signatureDate></ownerSignature></ownershipDocument>

