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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-08-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001200474</rptOwnerCik>
            <rptOwnerName>TRIEBES KARL D</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, Product Development &amp; CTO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                    <footnoteId id="F1"/>
                </transactionShares>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
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                <value></value>
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    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
                <footnoteId id="F5"/>
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                <value>0.00</value>
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                <value>2012-08-01</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>719</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>719</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12879</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
                <footnoteId id="F5"/>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-08-01</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>676</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>676</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5410</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
                <footnoteId id="F5"/>
            </securityTitle>
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                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-08-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>394</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <footnoteId id="F9"/>
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            <expirationDate>
                <footnoteId id="F7"/>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                    <value>394</value>
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                    <value>3546</value>
                </sharesOwnedFollowingTransaction>
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        </derivativeTransaction>
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    <footnotes>
        <footnote id="F1">Shares acquired based on performance targets for the August 2, 2010, August 1, 2011, and November 9, 2011 awards of Restricted Stock Units.</footnote>
        <footnote id="F2">Shares acquired upon vesting of the August 2, 2010, August 1, 2011, and November 9, 2011 awards of service-based Restricted Stock Units.</footnote>
        <footnote id="F3">This transaction was executed pursuant to a Rule 10b5-1 trading plan, in multiple trades at prices ranging from $93.02 to $93.97. 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 $94.10 to $94.20.  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">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="F6">8,635 of the service-based Restricted Stock Units awarded August 2, 2010 vest in twelve equal quarterly increments beginning November 1, 2010; an additional 10,000 Restricted Stock Units vest August 1, 2013.</footnote>
        <footnote id="F7">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="F8">The August 1, 2011 award of service-based Restricted Stock Units vests in twelve equal quarterly increments beginning November 1, 2011.</footnote>
        <footnote id="F9">The November 9, 2011 award of service-based Restricted Stock Units vest in twelve equal quarterly increments beginning February 1, 2012.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jeffrey A. Christianson by Power of Attorney</signatureName>
        <signatureDate>2012-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
