<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-08</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>4.71</value></conversionOrExercisePrice><transactionDate><value>2003-08-08</value></transactionDate><transactionCoding><transactionFormType>5</transactionFormType><transactionCode>J</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value>E</value></transactionTimeliness><transactionAmounts><transactionShares><value>511.0926</value></transactionShares><transactionPricePerShare><value>4.71</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>511.0926</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>43040.1766</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Options</value></securityTitle><conversionOrExercisePrice><value>3.6</value></conversionOrExercisePrice><transactionDate><value>2003-08-20</value><footnoteId id="F3" /></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>J</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F4" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>100000</value></transactionShares><transactionPricePerShare><value>3.6</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F5" /></exerciseDate><expirationDate><value>2010-11-21</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>100000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>952566</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></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">These options were granted as performance options on 11/21/2002 contingent upon the Company achieving certain financial performance objectives during the fourth quarter of fiscal year 2003.  The Board of Directors determined on 8/20/2003 that the contingent conditions had been met and the options were issued.</footnote><footnote id="F4">Options (right to buy) acquired through C-COR.net Corp.'s Incentive Plan.  </footnote><footnote id="F5">These options vest in four equal annual installments of 25,000 on the anniversary date of the grant.  These first vesting date is 11/21/2003.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>David A. Woodle</signatureName><signatureDate>2003-08-21</signatureDate></ownerSignature></ownershipDocument>

