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<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-11-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001048695</issuerCik>
        <issuerName>F5 NETWORKS INC</issuerName>
        <issuerTradingSymbol>FFIV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001684581</rptOwnerCik>
            <rptOwnerName>Kearny Ryan C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O F5 NETWORKS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>401 ELLIOTT AVE. W.</rptOwnerStreet2>
            <rptOwnerCity>SEATTLE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98119</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
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            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CTO &amp; SVP, Product Development</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <transactionPricePerShare>
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                <transactionPricePerShare>
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            <transactionDate>
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            <transactionTimeliness>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>179.0761</value>
                    <footnoteId id="F5"/>
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                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
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            <transactionCoding>
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            <transactionTimeliness>
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                <transactionPricePerShare>
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                    <footnoteId id="F6"/>
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    </nonDerivativeTable>

    <derivativeTable>
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                <footnoteId id="F7"/>
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                <transactionCode>M</transactionCode>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>343</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
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            <expirationDate>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>343</value>
                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
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                <footnoteId id="F7"/>
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            <transactionDate>
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                <value></value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <underlyingSecurityShares>
                    <value>7301</value>
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                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit</value>
                <footnoteId id="F7"/>
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            <transactionDate>
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            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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                    <value>388</value>
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                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
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            <expirationDate>
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            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>388</value>
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                <sharesOwnedFollowingTransaction>
                    <value>4665</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit</value>
                <footnoteId id="F7"/>
                <footnoteId id="F12"/>
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            <conversionOrExercisePrice>
                <value>0.00</value>
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            <transactionDate>
                <value>2018-11-01</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>4188</value>
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                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            <exerciseDate>
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            <expirationDate>
                <footnoteId id="F9"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4188</value>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4188</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                    <value>D</value>
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    </derivativeTable>

    <footnotes>
        <footnote id="F1">Shares acquired upon vesting of the November 1, 2016 and November 1, 2017 awards of service-based Restricted Stock Units.</footnote>
        <footnote id="F2">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $174.72 to $175.60. The reported price is the weighted average sale price. The reporting person undertakes to provide to the Company, any security holder of the Company, or Securities and Exchange Commission staff, upon request, complete information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F3">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $175.86 to $176.82. The reported price is the weighted average sale price. The reporting person undertakes to provide to the Company, any security holder of the Company, or Securities and Exchange Commission staff, upon request, complete information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F4">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $177.86 to $178.83. The reported price is the weighted average sale price. The reporting person undertakes to provide to the Company, any security holder of the Company, or Securities and Exchange Commission staff, upon request, complete information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F5">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $178.86 to $179.23. The reported price is the weighted average sale price. The reporting person undertakes to provide to the Company, any security holder of the Company, or Securities and Exchange Commission staff, upon request, complete information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F6">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $176.86 to $177.83. The reported price is the weighted average sale price. The reporting person undertakes to provide to the Company, any security holder of the Company, or Securities and Exchange Commission staff, upon request, complete information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F7">Each Restricted Stock Unit represents a contingent right to receive one share of F5 Networks, Inc. Common Stock on the vest date.</footnote>
        <footnote id="F8">This November 1, 2016 award of service-based Restricted Stock Units vests in sixteen equal quarterly increments beginning February 1, 2017.</footnote>
        <footnote id="F9">If the reporting person continues to provide services to the Company through the vest date, the corresponding number of shares of Common Stock of F5 Networks, Inc. will be issued to the reporting person on the vest date.</footnote>
        <footnote id="F10">This November 1, 2016 award of service-based Restricted Stock Units vests 100% on November 1, 2018.</footnote>
        <footnote id="F11">This November 1, 2017 award of service-based Restricted Stock Units vests in sixteen equal quarterly increments beginning February 1, 2018.</footnote>
        <footnote id="F12">Concurrent with the award of 4,188 service-based Restricted Stock Units, the Company granted the reporting person additional Restricted Stock Units that vest based on performance targets (&quot;Performance RSUs&quot;). If the performance targets are achieved at 100%, the reporting person will receive 4,188 Performance RSUs over the vesting period; the actual number of Performance RSUs received may be more or less depending on whether and to the extent that performance is greater than or less than targets. The Performance RSUs vests over a three-year period in three equal annual installments. Performance RSUs are not reported in Table II; the underlying shares of Performance RSUs will be reported in Table I if and when the Compensation Committee of the Board of Directors determines that the performance targets have been achieved.</footnote>
        <footnote id="F13">This November 1, 2018 award of service-based Restricted Stock Units vests in twelve equal quarterly increments beginning February 1, 2019.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Scot F. Rogers by Power of Attorney</signatureName>
        <signatureDate>2018-11-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
