<?xml version="1.0"?><ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-09-05</periodOfReport><notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0001062047</issuerCik>
        <issuerName>CONVERGYS CORP</issuerName>
        <issuerTradingSymbol>CVG</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001184862</rptOwnerCik>
            <rptOwnerName>FREKER JOHN C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>201 EAST FOURTH STREET</rptOwnerStreet1>
            <rptOwnerStreet2>PO BOX 1638</rptOwnerStreet2>
            <rptOwnerCity>CINCINNATI</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>45201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>President CMG</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Shares</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>85795</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common Shares</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>741.747</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trustee of ESPP</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeTransaction><securityTitle><value>Common Shares</value></securityTitle><transactionDate><value>2003-09-05</value></transactionDate><deemedExecutionDate><value>2003-09-05</value></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>6.984</value></transactionShares><transactionPricePerShare><value>18.65</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1109.743</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trustee of RSP</value><footnoteId id="F1" /></natureOfOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Option</value><footnoteId id="F2" /><footnoteId id="F3" /></securityTitle><conversionOrExercisePrice><value>0</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F4" /></exerciseDate><expirationDate><footnoteId id="F4" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>0</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>239892</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeTransaction><securityTitle><value>Phantom Share Unit</value><footnoteId id="F5" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F6" /></conversionOrExercisePrice><transactionDate><value>2003-09-05</value></transactionDate><deemedExecutionDate><value>2003-09-05</value></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>62.156</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F5" /></exerciseDate><expirationDate><footnoteId id="F5" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>62.156</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>6310.344</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Common shares balance held in Retirement Savings Plan.
</footnote><footnote id="F2">Option shares granted under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.</footnote><footnote id="F3">Right to buy.</footnote><footnote id="F4">Option shares granted on various dates under the Convergys 1998 Long Term Incentive Plan, which is a Rule 16b-3 Plan.</footnote><footnote id="F5">Acquired on various dates between January 1 and September 5, 2003 pursuant to the Convergys Corporation Executive Deferred Compensation Plan, at prices ranging from $11.30 and $18.91 per share.  Phantom shares are payable in cash or common shares of the Company upon termination of employment.</footnote><footnote id="F6">Security converts to common stock on a one-for-one basis.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ John C. Freker</signatureName><signatureDate>2003-09-08</signatureDate></ownerSignature></ownershipDocument>

