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        <issuerTradingSymbol>BA</issuerTradingSymbol>
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            <rptOwnerState>IL</rptOwnerState>
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            <officerTitle>Sr. VP, Internal Services</officerTitle>
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    <footnotes>
        <footnote id="F1">Includes adjustments for dividends accrued</footnote>
        <footnote id="F2">Performance shares convert on 1 for 1 basis on vesting</footnote>
        <footnote id="F3">2003 Performance Shares vest in the following installments when the average daily closing price of Boeing stock reaches, for a specified period, the following dollar levels:  15% at $42.38, 30% at $45.41, 45% at $48.43, 60% at $51.46, 75% at $54.49, 90% at $57.51, 100% at $60.54, 110% at $63.57, 120% at $66.59, and 125% at $68.11.</footnote>
        <footnote id="F4">Dividend allocated to Performance Share Account under the Deferred Compensation Plan.</footnote>
        <footnote id="F5">Phantom stock units are convertible into common stock on a 1-for-1 basis.</footnote>
        <footnote id="F6">Phantom stock units acquired by reporting person pursuant to the Company's Deferred Compensation Plan.  Units are payable in stock or cash following termination for retirement, death, disability or layoff.  Company match contributions are forfeited upon termination for any reason other than retirement, death, disability or layoff.</footnote>
        <footnote id="F7">Performance Share company match allocated to reporting person's performance share account under the deferred compensation plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: /s/ Mark R. Pacioni as Attorney-in-Fact</signatureName>
        <signatureDate>2005-06-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
