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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2004-06-28</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000888471</issuerCik>
        <issuerName>NESTOR PARTNERS</issuerName>
        <issuerTradingSymbol>None</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001294575</rptOwnerCik>
            <rptOwnerName>Crapple George E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE MILLBURN CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>1270 AVENUE OF THE AMERICAS, 11TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10020</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>See Remarks Below.</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Limited Partnership Interests</value>
            </securityTitle>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>12918</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Limited Partnership Interests</value>
            </securityTitle>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>1875973</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Self Through The Millburn Corporation Profit Sharing and 401(k) Savings Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Limited Partnership Interests</value>
            </securityTitle>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>2172485</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>As Trustee for Beker Family 1993 Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Limited Partnership Interests</value>
            </securityTitle>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>247182</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <remarks>Mr. Crapple serves as the Co-Chief Executive Officer and Co-Chairman of Millburn Ridgefield Corporation, the general partner of the Issuer.</remarks>

    <ownerSignature>
        <signatureName>George E Crapple</signatureName>
        <signatureDate>2004-06-28</signatureDate>
    </ownerSignature>
</ownershipDocument>

