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

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-04-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001234349</rptOwnerCik>
            <rptOwnerName>REILLY JAMES G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MARK R. MANLEY</rptOwnerStreet1>
            <rptOwnerStreet2>ALLIANCE CAPITAL MANAGEMENT CORPORATION</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 of General Partner</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Units rep. assign. of beneficial ownership of l.p. interests</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2004-04-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>107095</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>420823</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 was awarded 107,095 restricted Holding Units under the Amended and Restated Alliance Partners Compensation Plan.  The award vests in equal annual increments on each of December 1, 2004, 2005, 2006 and 2007 and will be paid to Reporting Person as vesting occurs, unless Reporting Person defers payment.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Adam Spilka, by pwr. att'y</signatureName>
        <signatureDate>2004-04-02</signatureDate>
    </ownerSignature>
</ownershipDocument>

