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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-03-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001283140</issuerCik>
        <issuerName>HOLLY ENERGY PARTNERS LP</issuerName>
        <issuerTradingSymbol>HEP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001482298</rptOwnerCik>
            <rptOwnerName>Cunningham Mark T.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2828 N. HARWOOD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1300</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Sr Vice President, Operations</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2013-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5049</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31371</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units</value>
            </securityTitle>
            <transactionDate>
                <value>2013-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5194</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>40.7478</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26177</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Restricted Units granted under the Holly Energy Partners, L.P. Long-Term Incentive Plan.</footnote>
        <footnote id="F2">The reporting person's ownership was adjusted to reflect the 2-for-1 unit split of Holly Energy Partners, L.P. common units, which occurred on January 16, 2013.</footnote>
        <footnote id="F3">The price reported is the weighted average sale price for the 5194 units sold.  The sale prices ranged from a low of $40.69 per unit to a high of $40.75 per unit.  The reporting person undertakes to provide to Holly Energy Partners, L.P., any security holder of Holly Energy Partners, L.P., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of units sold at each separate price within the range set forth in this footnote.</footnote>
    </footnotes>

    <remarks>Mr. Cunningham is Senior Vice President, Operations of Holly Logistic Services, L.L.C. Holly Logistic Services, L.L.C. is the general partner of HEP Logistics Holdings, L.P., the general partner of the Issuer.</remarks>

    <ownerSignature>
        <signatureName>Walter W. Zimmerman, Attorney in Fact</signatureName>
        <signatureDate>2013-03-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
