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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-11-07</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000028412</issuerCik>
        <issuerName>COMERICA INC /NEW/</issuerName>
        <issuerTradingSymbol>CMA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001520421</rptOwnerCik>
            <rptOwnerName>Smith Barbara</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1717 MAIN STREET</rptOwnerStreet1>
            <rptOwnerStreet2>MC 6404</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>EXHIBIT 24 - POWER OF ATTORNEY FOR BARBARA R. SMITH</remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer S. Perry, on behalf of Barbara R. Smith</signatureName>
        <signatureDate>2017-11-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
