<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
    <periodOfReport>2003-10-10</periodOfReport>
    <notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000320187</issuerCik>
        <issuerName>NIKE INC</issuerName>
        <issuerTradingSymbol>nke</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001239009</rptOwnerCik>
            <rptOwnerName>VAN PAASSCHEN FRITS D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE BOWERMAN DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BEAVERTON</rptOwnerCity>
            <rptOwnerState>OR</rptOwnerState>
            <rptOwnerZipCode>97005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>
  <nonDerivativeTable>
   <nonDerivativeTransaction>
      <securityTitle>
          <value>Class B Common Stock</value>
      </securityTitle>
      <transactionDate>
          <value>2003-10-21</value>
      </transactionDate>
      <deemedExecutionDate>
          <value>2003-10-21</value>
      </deemedExecutionDate>
      <transactionCoding>
          <transactionFormType>4</transactionFormType>
          <transactionCode>X</transactionCode>
          <equitySwapInvolved>0</equitySwapInvolved>
      </transactionCoding>
      <transactionTimeliness>
      <value />
      </transactionTimeliness>
      <transactionAmounts>
          <transactionShares>
              <value>18750</value>
              <footnoteId id="F1" />
          </transactionShares>
          <transactionPricePerShare>
              <value>0.00</value>
          </transactionPricePerShare>
          <transactionAcquiredDisposedCode>
              <value>A</value>
          </transactionAcquiredDisposedCode>
      </transactionAmounts>
      <postTransactionAmounts>
          <sharesOwnedFollowingTransaction>
              <value>31164</value>
          </sharesOwnedFollowingTransaction>
      </postTransactionAmounts>
      <ownershipNature>
          <directOrIndirectOwnership>
              <value>D</value>
          </directOrIndirectOwnership>
      </ownershipNature>
   </nonDerivativeTransaction>
   <nonDerivativeTransaction>
      <securityTitle>
          <value>Class B Common Stock</value>
      </securityTitle>
      <transactionDate>
          <value>2003-10-21</value>
      </transactionDate>
      <deemedExecutionDate>
          <value>2003-10-21</value>
      </deemedExecutionDate>
      <transactionCoding>
          <transactionFormType>4</transactionFormType>
          <transactionCode>S</transactionCode>
          <equitySwapInvolved>0</equitySwapInvolved>
      </transactionCoding>
      <transactionTimeliness>
      <value />
      </transactionTimeliness>
      <transactionAmounts>
          <transactionShares>
              <value>18750</value>
              <footnoteId id="F1" />
          </transactionShares>
          <transactionPricePerShare>
              <value>63.50</value>
          </transactionPricePerShare>
          <transactionAcquiredDisposedCode>
              <value>D</value>
          </transactionAcquiredDisposedCode>
      </transactionAmounts>
      <postTransactionAmounts>
          <sharesOwnedFollowingTransaction>
              <value>12414</value>
              <footnoteId id="F2" />
          </sharesOwnedFollowingTransaction>
      </postTransactionAmounts>
      <ownershipNature>
          <directOrIndirectOwnership>
              <value>D</value>
          </directOrIndirectOwnership>
      </ownershipNature>
   </nonDerivativeTransaction>
   <nonDerivativeTransaction>
      <securityTitle>
          <value>Class B Common Stock</value>
      </securityTitle>
      <transactionDate>
          <value>2003-10-10</value>
      </transactionDate>
      <deemedExecutionDate>
          <value>2003-10-10</value>
      </deemedExecutionDate>
      <transactionCoding>
          <transactionFormType>4</transactionFormType>
          <transactionCode>S</transactionCode>
          <equitySwapInvolved>0</equitySwapInvolved>
      </transactionCoding>
      <transactionTimeliness>
      <value />
      </transactionTimeliness>
      <transactionAmounts>
          <transactionShares>
              <value>156</value>
              <footnoteId id="F1" />
          </transactionShares>
          <transactionPricePerShare>
              <value>63.69</value>
          </transactionPricePerShare>
          <transactionAcquiredDisposedCode>
              <value>D</value>
          </transactionAcquiredDisposedCode>
      </transactionAmounts>
      <postTransactionAmounts>
          <sharesOwnedFollowingTransaction>
              <value>0</value>
          </sharesOwnedFollowingTransaction>
      </postTransactionAmounts>
      <ownershipNature>
          <directOrIndirectOwnership>
              <value>I</value>
          </directOrIndirectOwnership>
          <natureOfOwnership>
              <value>ESPP</value>
              <footnoteId id="F3" />
          </natureOfOwnership>
      </ownershipNature>
   </nonDerivativeTransaction>
    <nonDerivativeHolding>
      <securityTitle>
          <value>Class B Common Stock</value>
      </securityTitle>
      <postTransactionAmounts>
          <sharesOwnedFollowingTransaction>
              <value>610</value>
          </sharesOwnedFollowingTransaction>
      </postTransactionAmounts>
      <ownershipNature>
          <directOrIndirectOwnership>
              <value>I</value>
          </directOrIndirectOwnership>
          <natureOfOwnership>
              <value>Retirement Plan</value>
              <footnoteId id="F4" />
          </natureOfOwnership>
      </ownershipNature>
   </nonDerivativeHolding>
  </nonDerivativeTable>
  <derivativeTable>
   <derivativeTransaction>
      <securityTitle>
          <value>Employee Stock Option (right to buy)</value>
      </securityTitle>
      <conversionOrExercisePrice>
          <value>27.6875</value>
      </conversionOrExercisePrice>
      <transactionDate>
          <value>2003-10-21</value>
      </transactionDate>
      <deemedExecutionDate>
          <value>2003-10-21</value>
      </deemedExecutionDate>
      <transactionCoding>
          <transactionFormType>4</transactionFormType>
          <transactionCode>X</transactionCode>
          <equitySwapInvolved>0</equitySwapInvolved>
      </transactionCoding>
      <transactionAmounts>
          <transactionShares>
              <value>18750</value>
          </transactionShares>
          <transactionPricePerShare>
              <value>27.6875</value>
          </transactionPricePerShare>
          <transactionAcquiredDisposedCode>
              <value>D</value>
          </transactionAcquiredDisposedCode>
      </transactionAmounts>
      <exerciseDate>
          <value>2001-03-08</value>
              <footnoteId id="F5" />
      </exerciseDate>
      <expirationDate>
          <value>2010-03-07</value>
      </expirationDate>
      <underlyingSecurity>
          <underlyingSecurityTitle>
              <value>Class B Common Stock</value>
          </underlyingSecurityTitle>
          <underlyingSecurityShares>
              <value>18750</value>
          </underlyingSecurityShares>
      </underlyingSecurity>
      <postTransactionAmounts>
          <sharesOwnedFollowingTransaction>
              <value>6250</value>
          </sharesOwnedFollowingTransaction>
      </postTransactionAmounts>
      <ownershipNature>
          <directOrIndirectOwnership>
              <value>D</value>
          </directOrIndirectOwnership>
      </ownershipNature>
   </derivativeTransaction>
  </derivativeTable>
<footnotes>
   <footnote id="F1">Pursuant to Company policy, market sales of the Company stock by officers and directors are permitted only in quarterly window periods commencing on the third business day following each earnings release and ending 30 days later.          </footnote>
   <footnote id="F2">Includes 929 shares granted under the NIKE, Inc. Long Term Incentive Plan, and 11,485 shares granted under the NIKE, Inc. Stock I
ncentive Plan.</footnote>
   <footnote id="F3">Shares held in account under the NIKE, Inc. Employee Stock Purchase Plan.</footnote>
   <footnote id="F4">Shares in account under the NIKE, Inc. Retirement Savings Plan.</footnote>
   <footnote id="F5">Option granted for 25,000 shares on 3/8/2000 and became 25% exercisable on each of the first four anniversaries of the grant date
. </footnote>
</footnotes>
<remarks></remarks>    <ownerSignature>
       <signatureName>/s/John F. Coburn III on behalf of Frits D. van Paasschen</signatureName>
       <signatureDate>2003-10-22</signatureDate>
    </ownerSignature>
</ownershipDocument>

