<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0304</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2011-02-04</periodOfReport>

    <dateOfOriginalSubmission>2011-02-08</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001105033</rptOwnerCik>
            <rptOwnerName>CHRISTIANSON JEFFREY A</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 and General Counsel</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2011-02-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2134</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>120.15</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6439</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Sale pursuant to the terms of a 10b5-1 trading plan.</footnote>
        <footnote id="F2">Because of an administrative error, the reporting person's original Form 4 over-reported by 100 shares the sale of securities, and underreported by 100 shares the amount of securities beneficially owned following the reported transaction.  These 100 shares were also omitted from the holdings included in Form 4 reports subsequently filed by the reporting person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jeffrey A. Christianson</signatureName>
        <signatureDate>2012-02-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
