<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-13</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001130358</rptOwnerCik><rptOwnerName>COOK DONALD M JR</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>COMMODORE CLUB, SUITE 505</rptOwnerStreet1><rptOwnerStreet2>995 NORTH HIGHWAY A1A</rptOwnerStreet2><rptOwnerCity>INDIALANTIC</rptOwnerCity><rptOwnerState>FL</rptOwnerState><rptOwnerZipCode>32903</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-10-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1000</value></transactionShares><transactionPricePerShare><value>4.25</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>10000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Option</value></securityTitle><conversionOrExercisePrice><value>4.25</value></conversionOrExercisePrice><transactionDate><value>2003-10-13</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1000</value></transactionShares><transactionPricePerShare><value>4.25</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>1994-10-26</value></exerciseDate><expirationDate><value>2003-10-26</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>58500</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>Donald M. Cook</signatureName><signatureDate>2003-10-14</signatureDate></ownerSignature></ownershipDocument>

