<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-03-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000096831</issuerCik>
        <issuerName>TECUMSEH PRODUCTS CO</issuerName>
        <issuerTradingSymbol>TECUA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000920677</rptOwnerCik>
            <rptOwnerName>HERRICK FOUNDATION</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>150 W. JEFFERSON</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2500</rptOwnerStreet2>
            <rptOwnerCity>DETROIT</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48226</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Class A Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>194</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>41.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>406653</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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            </ownershipNature>
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        <nonDerivativeTransaction>
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            <transactionDate>
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            <deemedExecutionDate>
                <value>2005-03-02</value>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <transactionTimeliness>
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            </transactionTimeliness>
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                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>41.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <ownershipNature>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
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                <transactionAcquiredDisposedCode>
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        <nonDerivativeTransaction>
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            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
            <transactionCoding>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>405753</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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            <transactionDate>
                <value>2005-03-02</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>775</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>41.10</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>404978</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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            <deemedExecutionDate>
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            <transactionTimeliness>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <deemedExecutionDate>
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            <transactionTimeliness>
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            <transactionAmounts>
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                <transactionPricePerShare>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
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                <value></value>
            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>402647</value>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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                <value>Class B Common Stock, $1.00 par value</value>
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            <transactionDate>
                <value>2005-03-02</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>500</value>
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                <transactionPricePerShare>
                    <value>39.94</value>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1344400</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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                <value>Class B Common Stock, $1.00 par value</value>
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            <transactionDate>
                <value>2005-03-02</value>
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            <deemedExecutionDate>
                <value>2005-03-02</value>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>300</value>
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                <transactionPricePerShare>
                    <value>39.90</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                <sharesOwnedFollowingTransaction>
                    <value>1344100</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        <nonDerivativeTransaction>
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                <value>Class B Common Stock, $1.00 par value</value>
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            <transactionDate>
                <value>2005-03-02</value>
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                <value>2005-03-02</value>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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                    <value>575</value>
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                <transactionPricePerShare>
                    <value>39.85</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1343525</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2005-03-02</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.82</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1343325</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock, $1.00 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2005-03-02</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2005-03-02</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>39.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1343025</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James S. Nicholson
Herrick Foundation
By James S. Nicholson, Attorney-in-Fact</signatureName>
        <signatureDate>2005-03-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
