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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-09-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000777001</issuerCik>
        <issuerName>BEAR STEARNS COMPANIES INC</issuerName>
        <issuerTradingSymbol>BSC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001180139</rptOwnerCik>
            <rptOwnerName>SPECTOR WARREN J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BEAR, STEARNS &amp; CO. INC.</rptOwnerStreet1>
            <rptOwnerStreet2>383 MADISON AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10179</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Co-Pres./Co-COO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Fwd Purchase Contract (oblig. to sell)</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-09-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1893718</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2004-11-30</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2004-11-30</value>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1893718.00</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0.00</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On 9/704, the Reporting Person entered into a forward contract pursuant to the CAP Plan with The Bear Stearns Companies Inc. (BSC) in which the Reporting Person agreed to sell up to 1,893,718 common shares of BSC issuable upon settlement of CAP Units pursuant to the CAP Plan to BSC.  The forward contract is subject to BSCs satisfaction of certain performance goals. The forward contract will settle on 11/30/04.  The per share price will be the average of the Daily Volume Weighted Average Prices of the common stock on each day that it trades between $75 and $95 during the period from 9/7/04 through 11/29/04 (Included Days).  The number of shares purchased pursuant to the forward contract will be a fraction, the numerator of which is the number of Included Days and the denominator of which is the number of days the NYSE opens for trading between 9/7/04 and 11/29/04, multiplied by 1,893,718.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Warren J. Spector</signatureName>
        <signatureDate>2004-09-09</signatureDate>
    </ownerSignature>
</ownershipDocument>

