<?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>0001267380</rptOwnerCik><rptOwnerName>SHANER LANCE T</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>SHANER OFFICE BUILDING</rptOwnerStreet1><rptOwnerStreet2>1065 WADDLE ROAD</rptOwnerStreet2><rptOwnerCity>STATE COLLEGE</rptOwnerCity><rptOwnerState>PA</rptOwnerState><rptOwnerZipCode>16803</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>21000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Lion Venture Fund</value><footnoteId id="F1" /></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Options</value><footnoteId id="F2" /></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><footnoteId id="F2" /></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><footnoteId id="F2" /></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">Mr. Shaner has indirect beneficial ownership of 21,000 shares of common stock through his membership in Lion Venture Fund, LLC.</footnote><footnote id="F2">Options (right to buy) acquired through C-COR.net Corp.'s Incentive Plan.  </footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Lance T. Shaner</signatureName><signatureDate>2003-10-20</signatureDate></ownerSignature></ownershipDocument>

