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

    <documentType>4</documentType><periodOfReport>2003-12-19</periodOfReport><notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000096831</issuerCik>
        <issuerName>TECUMSEH PRODUCTS CO</issuerName>
        <issuerTradingSymbol>TECUA</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001196166</rptOwnerCik>
            <rptOwnerName>KAY DAVID W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>100 E. PATTERSON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>TECUMSEH</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>49286</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Vice President &amp; CFO</officerTitle></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Units</value><footnoteId id="F1" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F2" /></conversionOrExercisePrice><transactionDate><value>2003-12-19</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>0.6500</value></transactionShares><transactionPricePerShare><value>46.2700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2007-12-31</value></exerciseDate><expirationDate><value>2007-12-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Class A Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>0.6500</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2.8900</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Phantom Stock Units</value><footnoteId id="F3" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F2" /></conversionOrExercisePrice><transactionDate><value>2003-12-19</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>0.6500</value></transactionShares><transactionPricePerShare><value>46.2700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2005-12-31</value></exerciseDate><expirationDate><value>2005-12-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Class A Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>0.6500</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2.8900</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Phantom Stock Units</value><footnoteId id="F4" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F2" /></conversionOrExercisePrice><transactionDate><value>2003-12-19</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>0.8100</value></transactionShares><transactionPricePerShare><value>46.2700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2005-12-31</value></exerciseDate><expirationDate><value>2005-12-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Class A Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>0.8100</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>9.5100</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Phanton Stock Units</value><footnoteId id="F5" /></securityTitle><conversionOrExercisePrice><value>0</value><footnoteId id="F2" /></conversionOrExercisePrice><transactionDate><value>2003-12-19</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>0.8100</value></transactionShares><transactionPricePerShare><value>46.2700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-12-31</value></exerciseDate><expirationDate><value>2003-12-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Class A Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>0.8100</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>9.5100</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Additional Phantom Stock Units deemed acquired with the equivalent of dividends on Phantom Stock Units acquired during 2003 and payable 12/31/2007</footnote><footnote id="F2">Security converts to common stock on a one-for-one basis.</footnote><footnote id="F3">Additional Phantom Stock Units deemed acquired with the equivalent of dividends on Phantom Stock Units acquired during 2003 and payable 12/31/2005</footnote><footnote id="F4">Additional Phantom Stock Units deemed acquired with the equivalent of dividends on Phantom Stock Units acquired during 2001 and payable 12/31/2005</footnote><footnote id="F5">Additional Phantom Stock Units deemed acquired with the equivalent of dividends on Phantom Stock Units acquired during 2001 and payable 12/31/2003</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>David W. Kay
By Daryl P. McDonald, Attorney-in-Fact</signatureName><signatureDate>2003-12-22</signatureDate></ownerSignature></ownershipDocument>

