<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-10</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000110621</issuerCik><issuerName>RPM INTERNATIONAL INC/DE/</issuerName>        <issuerTradingSymbol>RPM</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001224021</rptOwnerCik><rptOwnerName>CARBONARI BRUCE A</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>25300 AL MOEN DRIVE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>NORTH OLMSTEAD</rptOwnerCity><rptOwnerState>OH</rptOwnerState><rptOwnerZipCode>44070</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, $0.01 par value</value></securityTitle><transactionDate><value>2003-10-10</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2400</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2400</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">Represents a grant of 2,400 shares of Common Stock issued pursuant to the RPM International Inc. 2003 Restricted Stock Plan for Directors.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Arthur C. Hall III as attorney-in-fact for Bruce A. Carbonari under Power of Attorney</signatureName><signatureDate>2003-10-10</signatureDate></ownerSignature></ownershipDocument>

