<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-28</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000895007</issuerCik><issuerName>WILLIAMS COAL SEAM GAS ROYALTY TRUST</issuerName>        <issuerTradingSymbol>WTU</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0000107263</rptOwnerCik><rptOwnerName>WILLIAMS COMPANIES INC</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>ONE WILLIAMS CENTER</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>TULSA</rptOwnerCity><rptOwnerState>OK</rptOwnerState><rptOwnerZipCode>74172</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>1</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Units</value></securityTitle><transactionDate><value>2003-08-28</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>4700</value></transactionShares><transactionPricePerShare><value>12.7798</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2264691</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Units</value></securityTitle><transactionDate><value>2003-08-29</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>7200</value></transactionShares><transactionPricePerShare><value>12.8725</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2257491</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>Cher S. Lawrence, Attorney-in-Fact for The Williams Companies, Inc.</signatureName><signatureDate>2003-09-02</signatureDate></ownerSignature></ownershipDocument>

