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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-12-10</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001193563</rptOwnerCik>
            <rptOwnerName>BERTRAND JAMES A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>DELPHI CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>5725 DELPHI DRIVE</rptOwnerStreet2>
            <rptOwnerCity>TROY</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48098-2815</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP &amp; Pres Auto Holdings Group</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2007-12-10</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2007-12-10</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6145</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>.24</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>98511</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>700</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Includes shares of restricted stock, which earn dividend equivalents in the form of additional shares as and when dividends are paid on the Issuer's common stock and which are subject to vesting over time and forfeiture, upon the occurence of certain events.  In October 2005 (the &quot;Filing Date&quot;), Issuer filed a voluntary petition for reorganization under Chapter 11 of the United States Bankruptcy Code.  Since the filing date, the Issuer has made no grants of equity awards and has not issued any stock in respect of previously granted awards, including the second installment of the 2003 and the first installment of the 2004 restricted stock unit awards, which vested on April 24, 2006 and May 7, 2007, respectively (the Undistributed Awards&quot;).  On December 10, 2007, the Issuer distributed shares in respect of the Undistributed Awards and the reporting person had shares withheld to pay withholding taxes.  Total holdings include shares of restricted stock acquired as a result of all previously reported awards, dividend equivalents earned through the date of this report on such prior awards, and direct holdings of Common Stock which are not restricted shares.</footnote>
        <footnote id="F2">Shares are held in a joint account with spouse.  Reporting person disclaims beneficial ownership with respect to the interest in the shares held by his spouse.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Marjorie Harris Loeb                                      James A. Bertrand, By: Marjorie Harris Loeb, pursuant to Power of Attorney</signatureName>
        <signatureDate>2007-12-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
