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

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-03-31</periodOfReport>

    <issuer>
        <issuerCik>0001072342</issuerCik>
        <issuerName>DELPHI CORP</issuerName>
        <issuerTradingSymbol>DPH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000942439</rptOwnerCik>
            <rptOwnerName>PENSKE ROGER S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5725 DELPHI DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>TROY</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48098</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-03-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3551</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.56</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>1988-08-08</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>1988-08-08</value>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3551</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>54777</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Phantom stock units acquired pursuant to Delphi's Deferred Compensation Plan for Non-Employee Directors.  Awards under the plan are settled in cash to participants upon retirement or other termination of service.  Non-employee directors are entitled to receive cash and phantom stock units as compensation for their service and may elect to defer receipt of the cash portion and receive additional phantom stock units in lieu thereof.  All of the issuer's non-employee directors, including the reporting person, have elected to receive all fees for the 2003 fiscal year in the form of phantom stock units.</footnote>
        <footnote id="F2">See footnote 1.</footnote>
        <footnote id="F3">Includes phantom stock units acquired as dividend equivalents on prior awards made pursuant to Delphi's Deferred Compensation Plan for Non-Employee Directors.  See previous footnotes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Roger S. Penske, by:  Diane Kaye, pursuant to Power of Attorney</signatureName>
        <signatureDate>2004-04-01</signatureDate>
    </ownerSignature>
</ownershipDocument>

