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

    <schemaVersion>X0202</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2007-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>0</form4TransactionsReported>

    <issuer>
        <issuerCik>0001042046</issuerCik>
        <issuerName>AMERICAN FINANCIAL GROUP INC</issuerName>
        <issuerTradingSymbol>AFG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000943521</rptOwnerCik>
            <rptOwnerName>LINDNER CARL H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE EAST FOURTH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CINCINNATI</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>45202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Chairman of the Board</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <value>Common Stock</value>
            </securityTitle>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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            <transactionTimeliness>
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            </transactionTimeliness>
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                </transactionShares>
                <transactionPricePerShare>
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        <nonDerivativeTransaction>
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        <nonDerivativeTransaction>
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        <nonDerivativeTransaction>
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        </nonDerivativeTransaction>
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            </transactionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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                <transactionShares>
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                <transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
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                <natureOfOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
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            <transactionDate>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
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            <transactionTimeliness>
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                <equitySwapInvolved>0</equitySwapInvolved>
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        </nonDerivativeTransaction>
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            <securityTitle>
                <value>Common Stock</value>
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                <equitySwapInvolved>0</equitySwapInvolved>
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                <value></value>
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                    <value>27.28</value>
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                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#3</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
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                <transactionPricePerShare>
                    <value>27.28</value>
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                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>4234</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#4</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
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                <transactionFormType></transactionFormType>
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                    <footnoteId id="F3"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#8</value>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
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            <transactionCoding>
                <transactionFormType></transactionFormType>
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            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#9</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Deferred Compensation</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>28.88</value>
            </conversionOrExercisePrice>
            <transactionCoding>
                <transactionFormType></transactionFormType>
            </transactionCoding>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>19956.716</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19956.716</value>
                    <footnoteId id="F8"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#1</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Indirect #1:  By Carl H. Lindner Jr., et al., TTEE for the CHL amended and Restated Family Trust dated 12/23/83.</footnote>
        <footnote id="F2">These shares were purchased through the Issuer's Dividend Reinvestment Plan.</footnote>
        <footnote id="F3">On October 4, 2007, Indirect #8 transferred 216,109 shares of the Company common stock to Indirect #2.</footnote>
        <footnote id="F4">Indirect #2:  By Edyth B. Lindner, Spouse.</footnote>
        <footnote id="F5">Indirect #3:  EBL TTEE of the Edyth B. Lindner Family Trust dated 4/13/04.</footnote>
        <footnote id="F6">Indirect #4:  By Carl H. Lindner, Jr., et al., Trustee of the CHL Amended and Restated Family Trust dated 1/22/82.</footnote>
        <footnote id="F7">Indirect #8:  By Joseph A. Pedoto, TTEE of the Edyth B. Lindner 2005-1 Qualified Annuity Trust dated 4/26/2005.</footnote>
        <footnote id="F8">Represents amounts deferred by the Reporting Person in the Issuer's Deferred Compensation Plan.  The account value increases or decreases based on the value of the Issuer's common stock.  Upon termination of employment or earlier, if so elected, the Reporting Person's account balance may be distributed, at the option of the Issuer, either in cash or in shares of the Issuer's common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Carl H. Lindner
By: Karl J. Grafe, as Attorney-in-Fact</signatureName>
        <signatureDate>2008-02-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
