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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-02-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000825313</issuerCik>
        <issuerName>ALLIANCE CAPITAL MANAGEMENT HOLDING LP</issuerName>
        <issuerTradingSymbol>AC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001296655</rptOwnerCik>
            <rptOwnerName>Cranch Laurence E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ALLIANCE CAPITAL MANAGEMENT CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>1345 AVENUE OF THE AMERICAS</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10105</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP and General Counsel of GP</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Units rep. assign. of beneficial ownership of l.p. interests</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2005-02-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>667</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Units representing assignments of beneficial ownership of limited partnership interests in Alliance Capital Management Holding L.
P. (&quot;Holding Units&quot;).</footnote>
        <footnote id="F2">Reporting Person allocated a portion of his 2004 award under the Amended and Restated Alliance Partners Compensation Plan to Holding Units.  In so doing, he acquired 667 restricted Holding Units.  The award vests (restrictions lapse) in equal annual increments on each of December 1, 2005, 2006, 2007, and 2008.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Adam Spilka, by pwr. att'y</signatureName>
        <signatureDate>2005-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
