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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001377480</rptOwnerCik>
            <rptOwnerName>Armario Jose</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AVON PRODUCTS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>1 AVON PLACE</rptOwnerStreet2>
            <rptOwnerCity>SUFFERN</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10901</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Deferred Stock Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3323.29</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.642</value>
                    <footnoteId id="F3"/>
                </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>3323.29</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100215.452</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Under the Board of Directors of Avon Products, Inc. Deferred Compensation Plan (the &quot;Plan&quot;) directors may defer receipt of quarterly fees into a cash account or an Avon stock unit account.  All amounts deferred are paid in cash upon termination of services as a director.</footnote>
        <footnote id="F2">Units correspond 1-for-1 with common stock.</footnote>
        <footnote id="F3">Pursuant to the Plan, the number of stock units credited quarterly is determined by dividing deferred quarterly fees by the average closing price of Avon stock during the last 10 trading days of such quarter.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Ginny Edwards, Attorney-In-Fact</signatureName>
        <signatureDate>2020-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
