<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-01</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001002811</issuerCik><issuerName>KENSEY NASH CORP</issuerName>        <issuerTradingSymbol>KNSY</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001008206</rptOwnerCik><rptOwnerName>NASH JOHN E</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>55 EAST UWCHLAN AVE.</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>EXTON</rptOwnerCity><rptOwnerState>PA</rptOwnerState><rptOwnerZipCode>19341</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>VP New Technologies</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-10-01</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2500</value></transactionShares><transactionPricePerShare><value>23.21</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>495000</value><footnoteId id="F2" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value><footnoteId id="F2" /></natureOfOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person in November 2001.</footnote><footnote id="F2">Shares held by John E. Nash Revocable Trust, of which the Reporting Person is Trustee, for the benefit of Reporting Person and his spouse.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ June Sheets, by power of attorney</signatureName><signatureDate>2003-10-07</signatureDate></ownerSignature></ownershipDocument>

