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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-05-25</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001200334</rptOwnerCik>
            <rptOwnerName>ANDERSON RICHARD H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2010-05-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1385209</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Mr. Anderson donated 1,000 shares of Delta common stock to The Delta Employee and Retiree Care Fund, a non-profit charitable organization.  The Fund was established in 2007 to provide financial assistance to eligible employees and retirees of Delta and its subsidiaries in the event of severe personal hardship, including those due to events such as natural disasters, fire, crime, death, illness or injury.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jan M. Davidson as attorney-in-fact for Richard H. Anderson</signatureName>
        <signatureDate>2010-05-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
