<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-14</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001180401</rptOwnerCik><rptOwnerName>ROYSE RODNEY M</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>23200 SW STAFFORD HILL DRIVE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>WEST LINN</rptOwnerCity><rptOwnerState>OR</rptOwnerState><rptOwnerZipCode>97068</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Option</value><footnoteId id="F1" /></securityTitle><conversionOrExercisePrice><value>7.78</value></conversionOrExercisePrice><transactionDate><value>2003-10-14</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>7500</value></transactionShares><transactionPricePerShare><value>7.78</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2004-10-14</value></exerciseDate><expirationDate><value>2011-10-14</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>7500</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>52500</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Options (right to buy) acquired through C-COR.net Corp.'s Incentive Plan.  </footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Rodney M. Royse</signatureName><signatureDate>2003-10-15</signatureDate></ownerSignature></ownershipDocument>

