<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>3</documentType><periodOfReport>2003-10-14</periodOfReport><noSecuritiesOwned>0</noSecuritiesOwned><issuer><issuerCik>0000350621</issuerCik><issuerName>C COR NET CORP</issuerName>        <issuerTradingSymbol>ccbl</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001190946</rptOwnerCik><rptOwnerName>IBARGUEN ANTHONY</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>SAFEGUARD SCIENTIFICS</rptOwnerStreet1><rptOwnerStreet2>435 DEVON PARK DRIVE #800</rptOwnerStreet2><rptOwnerCity>WAYNE</rptOwnerCity><rptOwnerState>PA</rptOwnerState><rptOwnerZipCode>19087</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeHolding><securityTitle><value>Options</value><footnoteId id="F1" /></securityTitle><conversionOrExercisePrice><value>7.78</value></conversionOrExercisePrice><exerciseDate><value>2003-10-14</value></exerciseDate><expirationDate><value>2011-10-14</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>10000</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Options</value></securityTitle><conversionOrExercisePrice><value>7.78</value></conversionOrExercisePrice><exerciseDate><value>2004-10-14</value></exerciseDate><expirationDate><value>2011-10-14</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>10000</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Options</value></securityTitle><conversionOrExercisePrice><value>7.78</value></conversionOrExercisePrice><exerciseDate><value>2005-10-14</value></exerciseDate><expirationDate><value>2011-10-14</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>10000</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Options (right to buy) acquired through C-COR.net Corp.'s Incentive Plan.  </footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Anthony A. Ibarguen</signatureName><signatureDate>2003-10-20</signatureDate></ownerSignature></ownershipDocument>

