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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-12-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001270610</rptOwnerCik>
            <rptOwnerName>FAY SHARON E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ADAM R. SPILKA</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></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Units of L.P. Interest in Alliance Capital Management L.P.</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-12-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8160000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Units rep. assign. of beneficial ownership of l.p. interests</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>8160000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16320000</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F6"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by SCB Partners</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The units of limited partnership interest in Alliance Capital Management L.P. (&quot;Alliance Units&quot;) are exchangable for units representing assignments of beneficial ownership of limited partnership interests in Alliance Capital Management Holding L.P. (&quot;Holding Units&quot;) upon the satisfaction of a number of conditions, including those listed in note 2.</footnote>
        <footnote id="F2">Conditions include: (i) the issuance of Holding Units must be exempt from registration pursuant to the Securities Act of 1933 and Holding must have received any necessary representations, opinions or other documentation in connection with such issuance; (ii) the issuance of Holding Units must be permissible under the Amended and Restated Agreement of Limited Partnership of Holding; (iii) AXA Equitable Life Insurance Company (f/k/a The Equitable Life Assurance Society of the United States, &quot;AELI&quot;) must consent to the transfer (which AXA Financial, Inc. (&quot;AXF&quot;), AELI's indirect parent, has agreed to cause AELI to do); and (iv) SCB Inc. (&quot;SCB&quot;) must provide an outside legal opinion, reasonably satisfactory to Alliance, stating that the exchange of Alliance Units for Holding Units constitutes a &quot;block transfer&quot; under U.S. Treasury regulations.</footnote>
        <footnote id="F3">As of the date hereof, the status of the foregoing conditions and their ability to be satisfied at the time of any proposed exchange is not certain.  Prior to any such exchange, neither SCB nor SCB Partners Inc. (&quot;Partners&quot;) is entitled to any rights as a unit holder of Holding.  In addition, the number of Holding Units into which the Alliance Units are exchangable is subject to adjustment for anti-dilution.</footnote>
        <footnote id="F4">On December 7, 2004, Partners delivered an exercise notice to AXF informing AXF of Partners' intention to require AXF (or its designee) to purchase 8,160,000 Alliance Units from Partners in accordance with the terms of a purchase agreement, dated as of June 20, 2000 (&quot;Purchase Agreement&quot;), among AXF, Alliance and SCB.  The purchase price for each Alliance Unit that may be sold to AXF pursuant to the Purchase Agreement upon delivery of such exercise notice will be the average of the closing prices of a Holding Unit as quoted on the NYSE Composite Transaction Tape for the ten trading days ending on the fifth trading day following December 7, 2004.  Upon purchase by AXF (or its desinee) of the 8,160,000 Alliance Units, Partners will hold 16,320,000 Alliance Units.</footnote>
        <footnote id="F5">Partners is a direct, wholly-owned subsidiary of SCB.  SCB, through its ownership of Partners, may be deemed to own beneficially and indirectly 16,320,000 Alliance Units following the transaction described herein.  SCB disclaims beneficial ownership of the securites reported herein except to the extent of its pecuniary interest therein.  SCB and Partners disclaim any beneficial ownership of the Holding Units that they are entitled to receive upon exchange of the Alliance Units because of the uncertainties described in notes 1, 2 and 3.  Upon such exchange, however, Partners would be deemed to own beneficially, and SCB may be deemed to own beneficially and indirectly, any such Holding Units into which Alliance Units are exchanged.  SCB would disclaim benefical ownership of such securities except to the extent of its pecuniary interest therein.</footnote>
        <footnote id="F6">Reporting Person, by being a stockholder of SCB, may be deemed to own beneficially and indirectly 16,320,000 Alliance Units following the transaction described herein.  Reporting Person disclaims beneficial ownership of the securities reported herein except to the extent of her pecuniary interest therein.  Reporting Person also disclaims beneficial ownership of the Holding Units that she is entitled to receive upon exchange of the Alliance Units because of the uncertainties described in notes 1, 2 and 3.  Upon such exchange, however, Reporting Person may be deemed to own beneficially and indirectly any such Holding Units into which Alliance Units are exchanged.  Reporting Person would disclaim beneficial ownership of such securities except to the extent of her pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Adam Spilka, by pwr. att'y</signatureName>
        <signatureDate>2004-12-09</signatureDate>
    </ownerSignature>
</ownershipDocument>

