<?xml version="1.0"?><ownershipDocument><schemaVersion>X0101</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-07-01</periodOfReport><issuer><issuerCik>0000052795</issuerCik><issuerName>ANIXTER INTERNATIONAL INC</issuerName>        <issuerTradingSymbol>AXE</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001233218</rptOwnerCik><rptOwnerName>ZELL MATTHEW</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>  </rptOwnerStreet1><rptOwnerStreet2>  </rptOwnerStreet2><rptOwnerCity>  </rptOwnerCity><rptOwnerState>  </rptOwnerState><rptOwnerZipCode>  </rptOwnerZipCode></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle></officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><nonDerivativeSecurity><securityTitle><value>Common Stock Units</value></securityTitle><transactionDate><value>2003-07-01</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>3804</value><footnoteId id="F1" /></transactionShares><transactionValue><value>0</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>14580</value><footnoteId id="F2" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value><footnoteId id="F3" /></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><footnotes><footnote id="F1">Stock units convert to common stock on a 1-for-1 basis at a time determined at the time of the grant.</footnote><footnote id="F2">Total includes 9,080 of common stock units and 5,500 shares of common stock held by the Matthew Zell Revocable Trust, of which Mr. Zell is the sole trustee and beneficiary.</footnote><footnote id="F3">5,500 shares of common stock are held by the Matthew Zell Revocable Trust, of which Mr. Zell is the sole trustee and beneficiary.</footnote></footnotes><ownerSignature><signatureName>Jim Knox, by power of attorney</signatureName><signatureDate>2003-07-02</signatureDate></ownerSignature></ownershipDocument>

