A new classification is proposed in which Bactritoidea and Ammonoidea are considered as subclasses. The subclass Bactritoidea
includes a single order, Bactritida. The subclass Ammonoidea includes ten orders: Anarcestida (suborders Agoniatitina, Auguritina,
Anarcestina, Gephurocerina, Timanocerina, and Prolecanitina), Tornocerida, Goniatitida (with suborders Goniatitina and Cyclolobina),
Praeglyphiocerida, Clymeniida (with suborders Gonioclymeniina and Clymeniina), Medlicottiida, Ceratitida (with suborders Paraceltitina,
Otocerina, Meekocerina, Sagecerina, Ptychitina, Ceratitina, Pinacocerina, Megaphyllitina, Arcestina, and Lobitina), Phyllocerida,
Lytocerida (with suborders Lytocerina and Turrilitina), and Ammonitida (with suborders Psilocerina, Haplocerina, Stephanocerina,
Cardiocerina, and Ancylocerina).