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

    <schemaVersion>X0303</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2008-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>1</form4TransactionsReported>

    <issuer>
        <issuerCik>0001030749</issuerCik>
        <issuerName>GULFMARK OFFSHORE INC</issuerName>
        <issuerTradingSymbol>GLF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001206112</rptOwnerCik>
            <rptOwnerName>LEECH JOHN E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1></rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity></rptOwnerCity>
            <rptOwnerState>X1</rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive V.P.-Operations</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-02-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>54.217</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>50.66</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>54.217</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26092.4</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-03-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1381.022</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>55.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1381.022</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27473.422</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-03-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>54.537</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>52.43</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>54.537</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27527.959</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
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            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-03-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>52.253</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27580.212</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-04-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>48.945</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>58.42</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>48.945</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27629.157</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-04-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>59.8</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>47.815</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27676.972</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-05-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>P</transactionCode>
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            </transactionCoding>
            <transactionTimeliness>
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            </transactionTimeliness>
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                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>61.930</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            </transactionAmounts>
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            <expirationDate>
                <footnoteId id="F1"/>
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            <underlyingSecurity>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
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            <transactionDate>
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                </transactionShares>
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                </transactionPricePerShare>
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        <derivativeTransaction>
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        <derivativeTransaction>
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                </transactionShares>
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        <derivativeTransaction>
            <securityTitle>
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            <transactionDate>
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            <transactionDate>
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                <value>L</value>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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            <transactionDate>
                <value>2008-10-31</value>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>77.280</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>37</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            <underlyingSecurity>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>28390.122</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
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            <transactionDate>
                <value>2008-11-15</value>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>28.37</value>
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                    <value>A</value>
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                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28490.91</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
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            <transactionDate>
                <value>2008-11-30</value>
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                <transactionFormType>4</transactionFormType>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>101.037</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>28.3</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>101.037</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>28591.947</value>
                </sharesOwnedFollowingTransaction>
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                    <value>D</value>
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            <transactionDate>
                <value>2008-12-15</value>
            </transactionDate>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>116.804</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.48</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>28708.751</value>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
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                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                    <value>A</value>
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                <footnoteId id="F1"/>
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                <footnoteId id="F1"/>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>28828.944</value>
                </sharesOwnedFollowingTransaction>
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                    <value>D</value>
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                <value>Phantom Stock</value>
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                <footnoteId id="F1"/>
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            <transactionDate>
                <value>2009-01-15</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>109.554</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>26.100</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                <footnoteId id="F1"/>
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            <expirationDate>
                <footnoteId id="F1"/>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>28938.498</value>
                </sharesOwnedFollowingTransaction>
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                    <value>D</value>
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                <value>Phantom Stock</value>
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            <transactionDate>
                <value>2009-01-31</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>119.439</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.940</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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            <expirationDate>
                <footnoteId id="F1"/>
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                <underlyingSecurityShares>
                    <value>119.439</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>29057.937</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
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                <footnoteId id="F1"/>
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            <transactionDate>
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            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
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                <transactionShares>
                    <value>109.178</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>26.190</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
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            <expirationDate>
                <footnoteId id="F1"/>
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                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>109.178</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>29167.115</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On reviewing the Section 16 reporting requirements relating to GulfMark Offshore, Inc.'s Executive Nonqualified Excess Plan, it was determined that the phantom stock units created by the deferral of compensation by both officers and directors should have been reported as a derivative security by the officer/director once the phantom stock unit was allocated to his account.  This filing reports all transactions related to the phantom stock units in the plan allocated to the individual from his point of entry into the plan through March 31, 2009.  Each phantom stock unit is the economic equivalent of one share of common stock.
Subject to the  provisions of the plan, the phantom stock units become payable only in common stock upon the officer/director's termination of service.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John Leech</signatureName>
        <signatureDate>2009-04-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
