-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 NdlFNnir/QvTgYX32YA/jVEAKhbwFlGmO6sTZ1G1JHqNLLsRSl5mjretyRnHqTLk
 lXuVTUuSIYe1jZc8NlTFLA==

<SEC-DOCUMENT>0000746838-04-000169.txt : 20040510
<SEC-HEADER>0000746838-04-000169.hdr.sgml : 20040510
<ACCEPTANCE-DATETIME>20040510160245
ACCESSION NUMBER:		0000746838-04-000169
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20040507
FILED AS OF DATE:		20040510

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			ALEXANDER LEIGH
		CENTRAL INDEX KEY:			0001185128

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-08729
		FILM NUMBER:		04793186

	MAIL ADDRESS:	
		STREET 1:		UNISYS CORPORATION
		STREET 2:		UNISYS WAY
		CITY:			BLUE BELL
		STATE:			PA
		ZIP:			19424-0001

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			UNISYS CORP
		CENTRAL INDEX KEY:			0000746838
		STANDARD INDUSTRIAL CLASSIFICATION:	SERVICES-COMPUTER INTEGRATED SYSTEMS DESIGN [7373]
		IRS NUMBER:				380387840
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		UNISYS WAY
		CITY:			BLUE BELL
		STATE:			PA
		ZIP:			19424
		BUSINESS PHONE:		2159864011

	MAIL ADDRESS:	
		STREET 1:		TOWNSHIP LINE & UNION MEETING ROADS
		CITY:			BLUE BELL
		STATE:			PA
		ZIP:			19424

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	BURROUGHS CORP /DE/
		DATE OF NAME CHANGE:	19861204
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>edgardoc.xml
<DESCRIPTION>PRIMARY DOCUMENT
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-05-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000746838</issuerCik>
        <issuerName>UNISYS CORP</issuerName>
        <issuerTradingSymbol>UIS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001185128</rptOwnerCik>
            <rptOwnerName>ALEXANDER LEIGH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>UNISYS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>UNISYS WAY</rptOwnerStreet2>
            <rptOwnerCity>BLUE BELL</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19424</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP &amp; Chief Marketing Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.415</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13362</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3362</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1146</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by USP Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>8.415</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-05-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2004-02-13</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-02-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Employee stock option granted under Rule 16b-3 Unisys Corporation 1990 Long-Term Incentive Plan.  The stock option is exercisable in four equal annual installments, commencing one year after the date of grant, February 13, 2003.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>By: Susan T. Keene, attorney-in-fact  For: Leigh Alexander</signatureName>
        <signatureDate>2004-05-10</signatureDate>
    </ownerSignature>
</ownershipDocument>

</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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