<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-11-03</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001130343</rptOwnerCik><rptOwnerName>HANELLY WILLIAM T</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>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>CFO, Secretary and Treasurer</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2500</value></transactionShares><transactionPricePerShare><value>5.125</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>8029</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>600</value></transactionShares><transactionPricePerShare><value>10.04</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>7429</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>661</value></transactionShares><transactionPricePerShare><value>10.05</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>6768</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>600</value></transactionShares><transactionPricePerShare><value>10.06</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>6168</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>139</value></transactionShares><transactionPricePerShare><value>10.08</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>6029</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>500</value></transactionShares><transactionPricePerShare><value>10.15</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5529</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2227.828</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value><footnoteId id="F3" /></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Option</value><footnoteId id="F4" /></securityTitle><conversionOrExercisePrice><value>5.125</value></conversionOrExercisePrice><transactionDate><value>2003-11-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2500</value></transactionShares><transactionPricePerShare><value>5.125</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2002-10-19</value></exerciseDate><expirationDate><value>2006-10-18</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>2500</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>227226</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeHolding><securityTitle><value>Phantom Stock</value><footnoteId id="F5" /></securityTitle><conversionOrExercisePrice><footnoteId id="F6" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F7" /></exerciseDate><expirationDate><footnoteId id="F7" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1386.032</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1386.032</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Acquired, pursuant to a 10b5-1 Sales Plan,through exercise of options acquired under C-COR.net Corp.'s Incentive Plan. </footnote><footnote id="F2">Sold pursuant to a 10b5-1 Sales Plan.</footnote><footnote id="F3">Shares acquired on various dates at various prices through C-COR.net Corp.'s 401K retirement plan.</footnote><footnote id="F4">Options (right to buy) acquired through C-COR.net Corp.'s Incentive Plan.  </footnote><footnote id="F5">Phantom Stock Unit acquired through C-COR.net Corp.'s non-qualified retirement savings and profit sharing plan.</footnote><footnote id="F6">Various, established on the date of each individual transaction under the retirement plan.</footnote><footnote id="F7">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></footnotes><remarks></remarks><ownerSignature><signatureName>William T. Hanelly</signatureName><signatureDate>2003-11-05</signatureDate></ownerSignature></ownershipDocument>

