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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-01-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000879575</issuerCik>
        <issuerName>TERRA NITROGEN CO L P /DE</issuerName>
        <issuerTradingSymbol>TNH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001230231</rptOwnerCik>
            <rptOwnerName>MEYER FRANCIS G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>600 FOURTH STREET</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 6000</rptOwnerStreet2>
            <rptOwnerCity>SIOUX CITY</rptOwnerCity>
            <rptOwnerState>IA</rptOwnerState>
            <rptOwnerZipCode>51102-6000</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2009-01-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1012.87</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>104.6533</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Phantom Unit</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1012.87</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1012.87</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2009-02-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>24.71</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>121.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Phantom Unit</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>24.71</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1037.58</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These units represent outside director's phantom unit awards under the Company's deferred compensation plan for outside directors, and are awarded each January 15.  The units along with accrued distributions are settled in cash on a one-for-one basis with the Company's common units one year following the data of award.</footnote>
        <footnote id="F2">These units represent cash distribution equivalents on the compensation plan for outside directors.  The units are settled in cash on January 15th of each calendar year.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>John W. Huey, by Power of Attorney for Francis G. Meyer</signatureName>
        <signatureDate>2009-03-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
