<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>5</documentType><periodOfReport>2003-06-27</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><form3HoldingsReported>1</form3HoldingsReported><form4TransactionsReported>0</form4TransactionsReported><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001130346</rptOwnerCik><rptOwnerName>ENG DAVID J</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>Corporate VP- Americas Bus.</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><transactionCoding><transactionFormType>3</transactionFormType></transactionCoding><postTransactionAmounts><sharesOwnedFollowingTransaction><value>4066.114</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><transactionCoding><transactionFormType>3</transactionFormType></transactionCoding><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5682</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Phantom Stock</value><footnoteId id="F2" /></securityTitle><conversionOrExercisePrice><footnoteId id="F3" /></conversionOrExercisePrice><transactionCoding><transactionFormType>3</transactionFormType></transactionCoding><exerciseDate><footnoteId id="F4" /></exerciseDate><expirationDate><footnoteId id="F4" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1824.129</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1824.129</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Options</value><footnoteId id="F5" /></securityTitle><conversionOrExercisePrice><footnoteId id="F6" /></conversionOrExercisePrice><transactionCoding><transactionFormType>3</transactionFormType></transactionCoding><exerciseDate><footnoteId id="F6" /></exerciseDate><expirationDate><footnoteId id="F6" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>230000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>230000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">The total holdings benefically owned indirectly by trust reported in Table I of this Form 5 show a total net decrease since the last report due to the addition of shares on various dates at various prices through C-COR.net Corp.'s 401K retirement plan and the reclassification of phantom stock units acquired under C-COR.net Corp.'s non-qualified retirement plan, that had been incorrectly reported on Table I as securities beneficially owned indireclty by trust.  The reclassified phantom stock units are now correctly reported as derivatives in Table II of this Form 5.</footnote><footnote id="F2">Phantom Stock Unit acquired on various dates and at various prices through C-COR.net Corp.'s non-qualified retirement savings and profit sharing plan. </footnote><footnote id="F3">Various, established on the date of each individual transaction under the retirement plan.</footnote><footnote id="F4">Not applicable.  Date not yet known.</footnote><footnote id="F5">Options (right to buy) acquired on various dates at various exercise prices through C-COR.net Corp.'s Incentive Plan.  </footnote><footnote id="F6">Various, according to the dates and terms of the individual grants comprising this holding.</footnote></footnotes><remarks>This Form 5 is submitted to correctly classify phantom stock units acquired on various dates at various prices under C-COR.net's non-quaified retirement plan as derivatives reportable on Table II rather than as securities shown in Table I, as previous reported.</remarks><ownerSignature><signatureName>David J. Eng</signatureName><signatureDate>2003-08-11</signatureDate></ownerSignature></ownershipDocument>

