<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="../4_X02.xsl"?><ownershipDocument>    <schemaVersion>X0202</schemaVersion>    <documentType>4</documentType>    <periodOfReport>2007-05-14</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>20330 STEVENS CREEK BOULEVARD</rptOwnerStreet1>            <rptOwnerStreet2></rptOwnerStreet2>            <rptOwnerCity>CUPERTINO</rptOwnerCity>            <rptOwnerState>CA</rptOwnerState>            <rptOwnerZipCode>95014</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>2007-05-14</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>M</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>20000</value>                </transactionShares>                <transactionPricePerShare>                    <value>6.4113</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>A</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>140583</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Stock</value>            </securityTitle>            <transactionDate>                <value>2007-05-14</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>16686</value>                </transactionShares>                <transactionPricePerShare>                    <value>19.55</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>123897</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Stock</value>            </securityTitle>            <transactionDate>                <value>2007-05-14</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>3314</value>                </transactionShares>                <transactionPricePerShare>                    <value>19.56</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>120583</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>    </nonDerivativeTable>    <derivativeTable>        <derivativeTransaction>            <securityTitle>                <value>Non-Qualified Stock Option (right to buy)</value>            </securityTitle>            <conversionOrExercisePrice>                <value>6.4113</value>            </conversionOrExercisePrice>            <transactionDate>                <value>2007-05-14</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>M</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>20000</value>                </transactionShares>                <transactionPricePerShare>                    <value>0.00</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <exerciseDate>                <footnoteId id="F2"/>            </exerciseDate>            <expirationDate>                <value>2011-04-17</value>            </expirationDate>            <underlyingSecurity>                <underlyingSecurityTitle>                    <value>Common Stock</value>                </underlyingSecurityTitle>                <underlyingSecurityShares>                    <value>20000</value>                </underlyingSecurityShares>            </underlyingSecurity>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>40000</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </derivativeTransaction>    </derivativeTable>    <footnotes>        <footnote id="F1">Sale was affected pursuant to a stock trading plan established under Rule 10b5-1.</footnote>        <footnote id="F2">25% vested on 1st anniversary measured from April 17, 2001 and the remainder vested in equal monthly installments over the next 36 months.</footnote>    </footnotes>    <remarks></remarks>    <ownerSignature>        <signatureName>/s/ Greg King, as attorney-in-fact for Robert S. Miller</signatureName>        <signatureDate>2007-05-16</signatureDate>    </ownerSignature></ownershipDocument>