<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2004-01-15</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000723531</issuerCik><issuerName>PAYCHEX INC</issuerName>        <issuerTradingSymbol>PAYX</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001228721</rptOwnerCik><rptOwnerName>SEBO J ROBERT</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>911 PANORAMA TRAIL S.</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>ROCHESTER</rptOwnerCity><rptOwnerState>NY</rptOwnerState><rptOwnerZipCode>14625</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>2004-01-15</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>G</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>4975.0000</value></transactionShares><transactionPricePerShare><value>35.1400</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>4776632.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>Jan Shuler, Attorney-in-fact</signatureName><signatureDate>2004-01-15</signatureDate></ownerSignature></ownershipDocument>

