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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-07-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000355766</issuerCik>
        <issuerName>HALLWOOD GROUP INC</issuerName>
        <issuerTradingSymbol>HWG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000733084</rptOwnerCik>
            <rptOwnerName>ALPHA TRUST /TX/</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O LE ROCCABELLA</rptOwnerStreet1>
            <rptOwnerStreet2>24 AVE BRINCESS GRACE</rptOwnerStreet2>
            <rptOwnerCity>MONTECARLO 98000</rptOwnerCity>
            <rptOwnerState>O9</rptOwnerState>
            <rptOwnerZipCode>MC98000</rptOwnerZipCode>
            <rptOwnerStateDescription>MONACO</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-07-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>851575</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>851575</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Hallwood Investments Limited</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">A discretionary beneficiary of The Alpha Trust (the &quot;Trust&quot;), contributed the shares to the Trust, which then contributed the
shares to Hallwood Investments Limited, which is wholly-owned by the Trust.</footnote>
        <footnote id="F2">N/A.</footnote>
    </footnotes>

    <remarks>THE ALPHA TRUST

By: HALLWOOD COMPANY LIMITED, trustee

By: /s/ Anthony J. Gumbiner
Anthony J. Gimbiner, Director
**Signature of Reporting Person</remarks>

    <ownerSignature>
        <signatureName>/s/ Anthony J. Gumbiner</signatureName>
        <signatureDate>2004-07-06</signatureDate>
    </ownerSignature>
</ownershipDocument>

