<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-03</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001062047</issuerCik><issuerName>CONVERGYS CORP</issuerName>        <issuerTradingSymbol>CVG</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001053484</rptOwnerCik><rptOwnerName>MASON STEVEN C</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>201 EAST FOURTH STREET</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>CINCINNATI</rptOwnerCity><rptOwnerState>OH</rptOwnerState><rptOwnerZipCode>45201</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Shares</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Option</value><footnoteId id="F1" /><footnoteId id="F2" /></securityTitle><conversionOrExercisePrice><value>0</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F3" /></exerciseDate><expirationDate><footnoteId id="F3" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>0</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>77300</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeTransaction><securityTitle><value>Phantom Share Unit</value><footnoteId id="F4" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F5" /></conversionOrExercisePrice><transactionDate><value>2003-10-03</value></transactionDate><deemedExecutionDate><value>2003-10-03</value></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>475.578</value></transactionShares><transactionPricePerShare><footnoteId id="F4" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F4" /></exerciseDate><expirationDate><footnoteId id="F4" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>475.578</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>8084.416</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Option shares granted under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.</footnote><footnote id="F2">Right to buy.</footnote><footnote id="F3">Option shares granted on various dates under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.</footnote><footnote id="F4">Acquired on various dates between January 1 and October 3, 2003 pursuant to the Convergys Corporation Executive Deferred Compensation Plan for Non-Employee Directors, at prices ranging from $11.30 and $19.68 per share.  Phantom shares are payable in cash or common shares of the Company upon termination of employment.</footnote><footnote id="F5">Security converts to common stock on a one-for-one basis.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Steven C. Mason</signatureName><signatureDate>2003-10-06</signatureDate></ownerSignature></ownershipDocument>

