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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2007-05-02</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000004447</issuerCik>
        <issuerName>HESS CORP</issuerName>
        <issuerTradingSymbol>HES</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001398313</rptOwnerCik>
            <rptOwnerName>John V Simon</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1185 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $1.00 par value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Savings Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.67</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1999-01-05</value>
            </exerciseDate>
            <expirationDate>
                <value>2008-01-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>13500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>16.40</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2000-02-03</value>
            </exerciseDate>
            <expirationDate>
                <value>2009-02-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.38</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2000-12-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2009-12-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>22500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>20.08</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2001-12-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2010-12-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.43</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2002-11-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2011-11-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>24.14</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2005-06-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-06-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>24.14</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2006-06-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-06-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>24.14</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2007-06-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-06-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.96</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2006-02-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-02-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.96</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2007-02-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-02-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.96</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2008-02-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-02-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>49.55</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2007-02-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-02-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>49.55</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2008-02-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-02-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>49.55</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2009-02-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-02-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>53.20</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2008-02-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-02-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>53.20</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2009-02-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-02-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Option to purchase Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>53.20</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2010-02-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-02-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Shares of restricted stock held in escrow under the Second Amended and Restated 1995 Long-Term Incentive Plan. The reporting person has only voting power of these shares until the lapsing of the period set by the Committee administering the plan at which time the shares plus accrued dividends will be delivered to the reporting person if he is still an employee of the Corporation.</footnote>
        <footnote id="F2">Shares held in Hess Corporation Savings and Stock Ownership Plan as of December 31, 2006.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>George C. Barry for John V. Simon</signatureName>
        <signatureDate>2007-05-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
