<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-09-02</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000943819</issuerCik>
        <issuerName>RESMED INC</issuerName>
        <issuerTradingSymbol>RMD</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001186102</rptOwnerCik>
            <rptOwnerName>FARRELL PETER C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>14040 DANIELSON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>POWAY</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92064</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector>
<isOfficer>1</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle>CEO</officerTitle>
<otherText></otherText>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeTable>
<nonDerivativeTransaction>
<securityTitle>
<value>ResMed Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-09-02</value>
<footnoteId id="F1"/>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>M</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>6200</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<value>13.3438</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>1035768</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeTransaction>
<securityTitle>
<value>ResMed Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-09-02</value>
<footnoteId id="F1"/>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>S</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>6200</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<value>42.979</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>D</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>1029568</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeTransaction>
<securityTitle>
<value>ResMed Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-09-02</value>
<footnoteId id="F1"/>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>S</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>2000</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<value>42.979</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>D</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>1027568</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeTransaction>
<securityTitle>
<value>ResMed Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-09-02</value>
<footnoteId id="F1"/>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>2000</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<value>43.005</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>D</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>1025568</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
</nonDerivativeTable>
<derivativeTable>
<derivativeTransaction>
<securityTitle>
<value>ResMed Common Stock (Options)</value>
</securityTitle>
<conversionOrExercisePrice>
<value>13.3438</value>
</conversionOrExercisePrice>
<transactionDate>
<value>2003-09-02</value>
<footnoteId id="F1"/>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>M</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>6200</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<value>0</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<exerciseDate>
<value>2000-07-30</value>
</exerciseDate>
<expirationDate>
<value>2009-07-30</value>
</expirationDate>
<underlyingSecurity>
<underlyingSecurityTitle>
<value>RMD Common Stock</value>
</underlyingSecurityTitle>
<underlyingSecurityShares>
<value>6200</value>
</underlyingSecurityShares>
</underlyingSecurity>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>303034</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</derivativeTransaction>
</derivativeTable>
<footnotes>
<footnote id="F1">All transactions were performed pursuant to an existing 10b5-1 plan.</footnote>
</footnotes>
<remarks></remarks>
<ownerSignature>
<signatureName>Peter C. Farrell</signatureName>
<signatureDate>2003-09-03</signatureDate>
</ownerSignature>
</ownershipDocument>

