<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-12-01</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000869487</issuerCik><issuerName>TANDY BRANDS ACCESSORIES INC</issuerName>        <issuerTradingSymbol>TBAC</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001200442</rptOwnerCik><rptOwnerName>FLAHERTY MARK J</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>690 EAST LAMAR BLVD., SUITE 200</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>ARLINGTON</rptOwnerCity><rptOwnerState>TX</rptOwnerState><rptOwnerZipCode>76011</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Chief Financial Officer</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock, $1.00 par value per share</value></securityTitle><transactionDate><value>2003-12-01</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>73.2600</value></transactionShares><transactionPricePerShare><value>15.0537</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1006.4850</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Stock Purchase Program</value></natureOfOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>Common Stock, $1.00 par value per share</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>528.8709</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value><footnoteId id="F2" /></directOrIndirectOwnership><natureOfOwnership><value>By 401(k) Plan</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common Stock, $1.00 par value per share</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>6509.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><footnotes><footnote id="F1">On December 1, 2003, the Tandy Brands Accessories, Inc. Stock Purchase Program purchased, in a transaction exempt under Rule 16b-3, 73.260 shares of common stock for the reporting person's account.  Such shares were purchased at approximately $15.0537 per share, the average of the closing prices of the common stock on the NASDAQ National Market System for each trading day in the month of November 2003 for which contributions were credited to the reporting person's account for the purchase of common stock.</footnote><footnote id="F2">Holdings reflect shares previously acquired under the Issuer's 401(k) Plan, also known as the Tandy Brands Accessories, Inc. Employees Investment Plan.  Holdings are as of November 30, 2003.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Mark J. Flaherty</signatureName><signatureDate>2003-12-02</signatureDate></ownerSignature></ownershipDocument>

