<?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>2003-05-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>108.806</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.94</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>108.806</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8508.635</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>2003-05-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>95.869</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.091</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>95.869</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8604.504</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>2003-06-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>97.327</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.82</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>97.327</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8701.831</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>2003-06-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>103.420</value>
                </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>103.420</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8805.251</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>2003-07-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>103.174</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.81</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>103.174</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8908.425</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>2003-07-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>123.004</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.1</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>123.004</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9031.429</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2003-08-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            </transactionAmounts>
            <exerciseDate>
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            <expirationDate>
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            <underlyingSecurity>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
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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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            <deemedExecutionDate></deemedExecutionDate>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>14</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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        <derivativeTransaction>
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                </transactionShares>
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        <derivativeTransaction>
            <securityTitle>
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            </securityTitle>
            <conversionOrExercisePrice>
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            <transactionDate>
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            <transactionAmounts>
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                </transactionShares>
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        <derivativeTransaction>
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                    <value>A</value>
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            <exerciseDate>
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            <expirationDate>
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                </transactionShares>
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        <derivativeTransaction>
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        <derivativeTransaction>
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            <conversionOrExercisePrice>
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            <transactionDate>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
                    <value>14.03</value>
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                <transactionAcquiredDisposedCode>
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            <exerciseDate>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
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                <value>L</value>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionShares>
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                <transactionPricePerShare>
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            <transactionDate>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>120.442</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.4</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10499.928</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
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            <conversionOrExercisePrice>
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            <transactionDate>
                <value>2004-02-15</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>114.328</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.17</value>
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                    <value>A</value>
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                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10614.256</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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                <value>Phantom Stock</value>
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                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-02-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>104.985</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.52</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
                    <value>104.985</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>10719.241</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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            <transactionDate>
                <value>2004-03-15</value>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>113.357</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.3</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>10832.598</value>
                </sharesOwnedFollowingTransaction>
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            <transactionDate>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>110.399</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.71</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
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                <footnoteId id="F1"/>
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                <footnoteId id="F1"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>10942.997</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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                <value>Phantom Stock</value>
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            <transactionDate>
                <value>2004-04-15</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100.252</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.3</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
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            <expirationDate>
                <footnoteId id="F1"/>
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            <underlyingSecurity>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>11043.249</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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            <securityTitle>
                <value>Phantom Stock</value>
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            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-04-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>114.858</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.1</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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                <underlyingSecurityTitle>
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                <underlyingSecurityShares>
                    <value>114.858</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>11158.107</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-05-15</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>127.152</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.64</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
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            <expirationDate>
                <footnoteId id="F1"/>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>127.152</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11285.259</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>
