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

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-02-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001234352</rptOwnerCik>
            <rptOwnerName>SHALETT LISA A</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></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Notional Interests in Alliance Capital Management L.P.</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-02-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5735</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>5735</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34065</value>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </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 footnote 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, as amended, and Alliance Capital Management Holding L.P. (&quot;Holding&quot;) 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, dated as of October 29, 1999; (iii) The Equitable Life Assurance Society of the U.S. (&quot;Equitable&quot;) must consent to the transfer (which AXA Financial, Inc. (&quot;AXF&quot;), Equitable's indirect parent, has agreed to cause Equitable to do); and (iv) SCB Inc. (&quot;SCB&quot;) must provide an outside legal opinion, reasonably satisfactory to Alliance Capital Management L.P. (&quot;Alliance&quot;), 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 exchange is not certain.  Prior to 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 February 20, 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 the delivery of such exercise notice will be the average 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 February 20, 2004.  Upon purchase by AXF (or its designee) of  the 8,160,000 Alliance Units, Partners will hold 24,480,000 Alliance Units.</footnote>
        <footnote id="F5">Reporting Person was granted an award that represented a notional interest in 39,800 Alliance Units that are held by Partners.  Such Alliance Units may be deemed to be derivative securities of Holding Units.  The value of Alliance Units may for some purposes be determined by reference to the price of Holding Units.  As a result of the transaction described in footnote 4, Reporting Person's notional interest was reduced by 5,735 Alliance Units, for which Reporting Person will receive cash consideration in accordance with the formula set forth in footnote 4.  Reporting person may be deemed to have an indirect interest in 34,065 Alliance Units or Holding Units.</footnote>
        <footnote id="F6">Partners is a direct, wholly-owned subsidiary of SCB.  SCB, through its ownership of Partners, may be deemed to own beneficially and indirectly 24,480,000 Alliance Units following the transaction described herein.  SCB disclaims beneficial ownership of the securities 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 footnotes 1, 2 and 3.  Upon such exchange, however, Partners would be deemed to own benefically and indirectly any such Holding Units into which Alliance Units are exchanged.  SCB would disclaim beneficial ownership of such securities except to the extent of its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Adam Spilka, by pwr. att'y</signatureName>
        <signatureDate>2004-02-24</signatureDate>
    </ownerSignature>
</ownershipDocument>

