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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-08-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000008868</issuerCik>
        <issuerName>AVON PRODUCTS INC</issuerName>
        <issuerTradingSymbol>AVP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001254583</rptOwnerCik>
            <rptOwnerName>MITAROTONDA JAMES A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BARINGTON CAPITAL GROUP, L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVENUE, 6TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-08-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.6909</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4057105</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Barington Companies Equity Partners, LP</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>264370</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Barington Companies Investors, LLC</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8333</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Reporting Person is the sole stockholder and director of LNA Capital Corp. LNA Capital Corp. is the general partner of Barington Capital Group, L.P., which is the majority member of Barington Companies Investors, LLC (&quot;Barington Investors&quot;). Barington Investors is the general partner of Barington Companies Equity Partners, L.P.</footnote>
        <footnote id="F2">The Reporting Person disclaims beneficial ownership of these securities, except to the extent of his pecuniary interest therein, and this report shall not be deemed to be an admission that the Reporting Person is the beneficial owner of these shares for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F3">The Reporting Person is the sole stockholder and director of LNA Capital Corp. LNA Capital Corp. is the general partner of Barington Capital Group, L.P., which is the majority member of Barington Investors. Barington Investors directly owns 101,821 shares of common stock of the Company. Barington Investors may also be deemed to beneficially own 162,549 shares of common stock of the Company as the investment advisor to a third party. Pursuant to the terms of an investment advisory agreement between Barington Investors and such party, Barington Investors manages an investment account that holds, among other things, 162,549 shares of common stock of the Company.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James A. Mitarotonda</signatureName>
        <signatureDate>2018-08-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
