<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-22</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001129623</issuerCik><issuerName>ODYSSEY HEALTHCARE INC</issuerName>        <issuerTradingSymbol>ODSY</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001227129</rptOwnerCik><rptOwnerName>BURNHAM RICHARD R</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>717 N. HARWOOD, SUITE 1500</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>DALLAS</rptOwnerCity><rptOwnerState>TX</rptOwnerState><rptOwnerZipCode>75201</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Chief Executive Officer</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock, par value $0.001 per share</value></securityTitle><transactionDate><value>2003-08-22</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>500</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>30.64</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>482432</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Employee Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>15.1533</value><footnoteId id="F1" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><value>2012-12-09</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><footnoteId id="F1" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>198756</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Employee Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>7.1866</value><footnoteId id="F1" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F3" /></exerciseDate><expirationDate><value>2011-11-16</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><footnoteId id="F1" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>196893</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Employee Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>0.4466</value><footnoteId id="F1" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F4" /></exerciseDate><expirationDate><value>2008-07-15</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><footnoteId id="F5" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>14143</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Employee Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>0.4466</value><footnoteId id="F1" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F6" /></exerciseDate><expirationDate><value>2010-01-25</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><footnoteId id="F5" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>117213</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Employee Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>1.38</value><footnoteId id="F1" /></conversionOrExercisePrice><exerciseDate><footnoteId id="F7" /></exerciseDate><expirationDate><value>2011-01-31</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><footnoteId id="F5" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>41625</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Reflects 50% stock dividend distributed on August 12, 2003 to stockholders of record on July 28, 2003.</footnote><footnote id="F2">1/48th of the stock options become exercisable on the 9th of each month, commencing January 9, 2003, with all stock options becoming fully exercisable on December 9, 2006.</footnote><footnote id="F3">1/48th of the stock options become exercisable on the 16th of each month, commencing December 9, 2001, with all stock options becoming fully exercisable on November 16, 2005.</footnote><footnote id="F4">20% of the stock options became exercisable on July 15, 1999, and 1/60th of the stock options become exercisable on the 15th of each month thereafter, commencing August 15, 1999, with all stock options becoming fully exercisable on July 15, 2003.</footnote><footnote id="F5">Upon the exercise of one stock option, the option holder will receive one share of common stock.</footnote><footnote id="F6">20% of the stock options became exercisable on January 25, 2001, and 1/60th of the stock options become exercisable on the 25th of each month thereafter, commencing February 25, 2001, with all stock options becoming fully exercisable on January 25, 2005.</footnote><footnote id="F7">20% of the stock options became exercisable on January 31, 2002, and 1/60th of the stock options become exercisable on the last day of each month thereafter, commencing February 28, 2002, with all stock options becoming fully exercisable on January 31, 2006.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Douglas B. Cannon, by power of attorney</signatureName><signatureDate>2003-08-26</signatureDate></ownerSignature></ownershipDocument>

