<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>3</documentType><periodOfReport>2003-07-29</periodOfReport><noSecuritiesOwned>0</noSecuritiesOwned><issuer><issuerCik>0000764065</issuerCik><issuerName>CLEVELAND CLIFFS INC</issuerName>        <issuerTradingSymbol>CLF</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001257528</rptOwnerCik><rptOwnerName>GALLAGHER DONALD J</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>1100 SUPERIOR AVENUE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>CLEVELAND</rptOwnerCity><rptOwnerState>OH</rptOwnerState><rptOwnerZipCode>44114</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Senior VP &amp; CFO &amp; Treasurer</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Shares</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1371</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common Shares</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>9271</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By VNQDC</value><footnoteId id="F1" /></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Options (right to buy)</value></securityTitle><conversionOrExercisePrice><footnoteId id="F2" /></conversionOrExercisePrice><exerciseDate><value>2003-01-12</value><footnoteId id="F2" /></exerciseDate><expirationDate><value>2009-01-12</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>10000</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Retention Units</value></securityTitle><conversionOrExercisePrice><footnoteId id="F4" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F3" /></exerciseDate><expirationDate><footnoteId id="F3" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>600</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Retention Units</value></securityTitle><conversionOrExercisePrice><footnoteId id="F4" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F5" /></exerciseDate><expirationDate><footnoteId id="F5" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>900</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Retention Units</value></securityTitle><conversionOrExercisePrice><footnoteId id="F4" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F6" /></exerciseDate><expirationDate><footnoteId id="F6" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Shares</value></underlyingSecurityTitle><underlyingSecurityShares><value>900</value></underlyingSecurityShares></underlyingSecurity><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Held for the benefit of the Reporting Person by the Cleveland-Cliffs Inc Voluntary Non-Qualified Deferred Compensation Plan (VNQDC).</footnote><footnote id="F2">On 1/12/99, options for 10,000 shares were granted to the reporting person under the Cleveland-Cliffs Inc 1992 Incentive Equity Plan (As amended and Restated as of May 13, 1997, as amended)("Plan").  One-third of such options are priced at $54.140625, one-third are priced at $64.96875, and one-third are priced at $75.796875.</footnote><footnote id="F3">Represents a grant of Retention Units to the Reporting Person under the Cleveland-Cliffs Inc Long-Term Incentive Program covering the period January 1, 2001 through December 31, 2003 (Incentive Period).  Payment of the Retention Units will be made in cash after the completion of the Incentive Period based upon the employment by the Company of the Reporting Person and the market value of a Common Share of the Company on the last day of the Incentive Period.</footnote><footnote id="F4">Converted common stock on a 1-for-1 basis.</footnote><footnote id="F5">Represents a grant of Retention Units to the Reporting Person under the Cleveland-Cliffs Inc Long-Term Incentive Program covering the period January 1, 2002 through December 31, 2004 (Incentive Period).  Payment of the Retention Units will be made in cash after the completion of the Incentive Period based upon the employment by the Company of the Reporting Person and the market value of a Common Share of the Company on the last day of the Incentive Period.</footnote><footnote id="F6">Represents a grant of Retention Units to the Reporting Person under the Cleveland-Cliffs Inc Long-Term Incentive Program covering the period January 1, 2003 through December 31, 2005 (Incentive Period).  Payment of the Retention Units will be made in cash after the completion of the Incentive Period based upon the employment by the Company of the Reporting Person and the market value of a Common Share of the Company on the last day of the Incentive Period.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Donald J. Gallagher</signatureName><signatureDate>2003-08-04</signatureDate></ownerSignature></ownershipDocument>

