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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-04-26</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001189310</rptOwnerCik>
            <rptOwnerName>DAWES ALAN S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>DELPHI CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>5725 DELPHI DRIVE</rptOwnerStreet2>
            <rptOwnerCity>TROY</rptOwnerCity>
            <rptOwnerState>MI</rptOwnerState>
            <rptOwnerZipCode>48098</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Chairman and Chief Financ</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-04-26</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-04-26</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4779</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.64</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>206836</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-04-26</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-04-26</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12543</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401(k) Plan</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </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.  On April 24, 2004, the first installment of the 2003 award of restricted stock vested and the reporting person had shares witheld to pay witholding 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">Not applicable.  No transaction has taken place.  See footnote No. 3.</footnote>
        <footnote id="F3">Shares held in trust under Delphi Stock Savings Plan, State Street Bank as trustee, and invested in the Delphi Stock Fund, an investment option under the 401(k) Plan.  Balance is as of March 31, 2004, the date of the last quarterly statement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Alan S. Dawes, by:  Diane L. Kaye, pursuant to Power of Attorney</signatureName>
        <signatureDate>2004-04-28</signatureDate>
    </ownerSignature>
</ownershipDocument>

