<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-18</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001130340</rptOwnerCik><rptOwnerName>WOODLE DAVID A</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>C/O C-COR.NET CORP.</rptOwnerStreet1><rptOwnerStreet2>60 DECIBEL ROAD</rptOwnerStreet2><rptOwnerCity>STATE COLLEGE</rptOwnerCity><rptOwnerState>PA</rptOwnerState><rptOwnerZipCode>16801</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>CEO and Chairman</officerTitle></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Unit</value></securityTitle><conversionOrExercisePrice><value>6.99</value></conversionOrExercisePrice><transactionDate><value>2003-08-18</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>J</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>345.3329</value></transactionShares><transactionPricePerShare><value>6.99</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><footnoteId id="F2" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>345.3329</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>41320.003</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></derivativeTransaction><derivativeHolding><securityTitle><value>Options</value></securityTitle><conversionOrExercisePrice><footnoteId id="F3" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F4" /></exerciseDate><expirationDate><footnoteId id="F5" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>952566</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>952566</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Phantom Stock Unit acquired through C-COR.net Corp.'s non-qualified retirement savings and profit sharing plan.</footnote><footnote id="F2">Date not yet known. These derivatives are exercisable upon the participant's retirement and may be taken in the form of stock or in cash.</footnote><footnote id="F3">Options (right to buy) acquired on various dates at various exercise prices through C-COR.net Corp.'s Incentive Plan.  </footnote><footnote id="F4">Various, according to the dates and terms of the individual grants comprising this holding.</footnote><footnote id="F5">Various, established on the date of each individual transaction under the retirement plan.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>David A. Woodle</signatureName><signatureDate>2003-09-19</signatureDate></ownerSignature></ownershipDocument>

