<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-22</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001015293</issuerCik><issuerName>HOUSTON EXPLORATION CO</issuerName>        <issuerTradingSymbol>THX</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001195164</rptOwnerCik><rptOwnerName>MCKESSY STEPHEN W</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>40 HUNTING RIDGE LANE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>WILTON</rptOwnerCity><rptOwnerState>CT</rptOwnerState><rptOwnerZipCode>06897</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>stock option (right to buy)</value></securityTitle><conversionOrExercisePrice><value>35.11</value></conversionOrExercisePrice><transactionDate><value>2003-09-22</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2000</value></transactionShares><transactionPricePerShare><value>35.11</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-09-22</value></exerciseDate><expirationDate><value>2013-09-22</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>2000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Stephen W. McKessy</signatureName><signatureDate>2003-09-24</signatureDate></ownerSignature></ownershipDocument>

