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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-04-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <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>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of the Board</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
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                    <value>#4</value>
                    <footnoteId id="F6"/>
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                <value>Common Stock</value>
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                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>#8</value>
                    <footnoteId id="F7"/>
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            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On April 12, 2006, Indirect #8 transferred 147,051 shares of the Company Common Stock to Indirect #2.  On April 26, 2006, the Reporting Person transferred 170 shares of the Company Common Stock to Indirect #1.</footnote>
        <footnote id="F2">These shares were purchased through the Issuer's Dividend Reinvestment Plan</footnote>
        <footnote id="F3">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="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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Carl H. Lindner,
By Karl J. Grafe, as Attorney-in-Fact</signatureName>
        <signatureDate>2006-06-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
