<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="../4_X02.xsl"?><ownershipDocument>    <schemaVersion>X0303</schemaVersion>    <documentType>4</documentType>    <periodOfReport>2010-12-15</periodOfReport>    <notSubjectToSection16>0</notSubjectToSection16>    <issuer>        <issuerCik>0000849399</issuerCik>        <issuerName>SYMANTEC CORP</issuerName>        <issuerTradingSymbol>SYMC</issuerTradingSymbol>    </issuer>    <reportingOwner>        <reportingOwnerId>            <rptOwnerCik>0001184215</rptOwnerCik>            <rptOwnerName>MILLER ROBERT STEVE</rptOwnerName>        </reportingOwnerId>        <reportingOwnerAddress>            <rptOwnerStreet1>350 ELLIS STREET</rptOwnerStreet1>            <rptOwnerStreet2></rptOwnerStreet2>            <rptOwnerCity>MOUNTAIN VIEW</rptOwnerCity>            <rptOwnerState>CA</rptOwnerState>            <rptOwnerZipCode>94043</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>2010-12-15</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>S</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>                <footnoteId id="F1"/>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>17000</value>                </transactionShares>                <transactionPricePerShare>                    <value>17.19</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>88555</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>    </nonDerivativeTable>    <footnotes>        <footnote id="F1">Sale was made pursuant to a stock trading plan established under Rule 10b5-1.</footnote>    </footnotes>    <remarks></remarks>    <ownerSignature>        <signatureName>/s/ Simona Katcher, as attorney-in-fact for Robert S. Miller</signatureName>        <signatureDate>2010-12-17</signatureDate>    </ownerSignature></ownershipDocument>