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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2006-09-01</periodOfReport>

    <dateOfOriginalSubmission>2006-09-05</dateOfOriginalSubmission>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001286086</issuerCik>
        <issuerName>BLUE ROCK MARKET NEUTRAL FUND LLC</issuerName>
        <issuerTradingSymbol>NONE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001374548</rptOwnerCik>
            <rptOwnerName>Blue Rock Core Fixed Income Portable Alpha Fund II L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>445 EAST LAKE STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 230</rptOwnerStreet2>
            <rptOwnerCity>WAYZATA</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55391</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Feeder into Master (1)</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Limited Liability Company Interests</value>
            </securityTitle>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>34750000</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <remarks>(1)  Blue Rock Core Fixed Income Portable Alpha Fund II, L.P. invests substantially all of its assets in Blue Rock Market
 Neutral  Fund, LLC, a Delaware Limited Liability Company, through a &quot;master-feeder&quot; arrangement.</remarks>

    <ownerSignature>
        <signatureName>/s/ Robert W. Fullerton</signatureName>
        <signatureDate>2006-09-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
