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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-06-03</periodOfReport>

    <issuer>
        <issuerCik>0000027904</issuerCik>
        <issuerName>DELTA AIR LINES INC /DE/</issuerName>
        <issuerTradingSymbol>DAL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001179811</rptOwnerCik>
            <rptOwnerName>MASSEY WALTER E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>DELTA AIR LINES, INC., DEPT. 981</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 20574</rptOwnerStreet2>
            <rptOwnerCity>ATLANTA</rptOwnerCity>
            <rptOwnerState>GA</rptOwnerState>
            <rptOwnerZipCode>30320</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-06-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8513</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Non-employee members of Delta's Board of Directors receive an annual restricted stock award of $40,000, based on current market prices.  The shares reported in this Form 4 represent the annual restricted stock grant to the Reporting Person, as approved by the Board of Directors on June 3, 2008.  The shares were acquired in a transaction exempt under Rule 16b-3(d).</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Nanci Oliver Sloan as attorney-in-fact for       Walter E. Massey</signatureName>
        <signatureDate>2008-06-05</signatureDate>
    </ownerSignature>
</ownershipDocument>

