<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-30</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001069183</issuerCik><issuerName>TASER INTERNATIONAL INC</issuerName>        <issuerTradingSymbol>TASR</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0000942521</rptOwnerCik><rptOwnerName>SMITH PHILLIPS W</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>7860 EAST MCCLAIN DRIVE</rptOwnerStreet1><rptOwnerStreet2>SUITE 2</rptOwnerStreet2><rptOwnerCity>SCOTTSDALE</rptOwnerCity><rptOwnerState>AZ</rptOwnerState><rptOwnerZipCode>85260</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>1</isTenPercentOwner><isOther>0</isOther><officerTitle>Chairman</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-10-30</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>6500</value></transactionShares><transactionPricePerShare><value>69</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>215529</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>/s/Phillips W. Smith, by Kathleen C. Hanrahan, Attorney-in-fact</signatureName><signatureDate>2003-10-31</signatureDate></ownerSignature></ownershipDocument>

