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<ownershipDocument>

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    <periodOfReport>2019-02-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001746640</rptOwnerCik>
            <rptOwnerName>WHALEN CHAD MICHAEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O F5 NETWORKS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>401 ELLIOTT AVE. WEST</rptOwnerStreet2>
            <rptOwnerCity>SEATTLE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98119</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Worldwide Sales</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <expirationDate>
                <footnoteId id="F5"/>
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                <underlyingSecurityShares>
                    <value>83</value>
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                <sharesOwnedFollowingTransaction>
                    <value>249</value>
                </sharesOwnedFollowingTransaction>
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        <derivativeTransaction>
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                <value>2019-02-01</value>
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                    <value>581</value>
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                    <value>0.00</value>
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                    <value>D</value>
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            <expirationDate>
                <footnoteId id="F5"/>
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                    <value>581</value>
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                <sharesOwnedFollowingTransaction>
                    <value>6399</value>
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    <footnotes>
        <footnote id="F1">Shares acquired upon vesting of the February 1, 2017, November 1, 2017, and November 1, 2018 awards of service-based Restricted Stock Units.</footnote>
        <footnote id="F2">This transaction was executed pursuant to a Rule 10b5-1 trading plan.</footnote>
        <footnote id="F3">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="F4">Twenty five percent (25%) of this February 1, 2017 award of service-based Restricted Stock Units vests on February 1, 2018, and the remaining seventy five percent (75%) vests in twelve equal quarterly increments beginning May 1, 2018</footnote>
        <footnote id="F5">If the reporting person continues to serve as an officer of the Company on 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="F6">The service-based Restricted Stock Units (RSUs) outstanding under this 11/01/2017 grant vest as follows: 83 vest 2/1/2019, 83 vest
05/01/2019, 83 vest 08/01/2019, 83 vest 11/01/2019.</footnote>
        <footnote id="F7">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/ Joseph P. McDermott by Power of Attorney</signatureName>
        <signatureDate>2019-02-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
