The Ammonoidea are thus classified by Dr. P. Fischer:—

(a) Retrosiphonata. Fam. 1. Goniatitidae.—Shell nautiloid, whorls sometimes disjoined, siphuncle ventral or dorsal, sutures simple. Principal genera: Clymenia, Goniatites (Fig. 258, A).—Devonian to Carboniferous.

(b) Prosiphonata. Fam. 2. Arcestidae.—Shell globular, smooth or striated and rayed, body-chamber very long, aperture often with a projecting hood, umbilicus closed by a callosity, lobes numerous, foliaceous, aptychus present. Principal genera: Arcestes, Lobites.—Principally Trias.

Fam. 3. Tropitidae.—Differs from Arcestidae mainly in the more highly ornamented surface, which is decorated with ribs which become granular at the periphery. Principal genus, Tropites.—Trias and Lias.

Fam. 4. Ceratitidae.—Shell ribbed and tuberculated, body-chamber short, lobes denticulated, saddles simple. Principal genera: Ceratites (Fig. 258, B), Trachyceras.—Principally Trias.

Fam. 5. Clydonitidae.—Shell variable in form, body-chamber short, sutural line undulated, simple. Principal genera: Clydonites, Choristoceras, Rhabdoceras, Cochloceras.—Trias.

Fam. 6. Pinacoceratidae.—Shell discoidal, usually smooth, body-chamber short, sutural line very complex, lobes numerous. Principal genera: Pinacoceras, Sageceras.—Carboniferous to Trias.

Fam. 7. Amaltheidae.—Shell broad, keeled, last whorl concealing most of the spire, sutures with auxiliary lobes, incised.—Principal genera: Amaltheus, Schloenbacia, Sphenodiscus.—Trias, Cretaceous.

Fam. 8. Ammonitidae.—Body-chamber long, whorls narrow, uncovered, more or less ribbed, aperture simple, sutural line normal, aptychus single, corneous. Principal genera: Ammonites, Aegoceras.—Principally Lias.

Fam. 9. Lytoceratidae.—Shell discoidal, body-chamber short, aperture simple, no aptychus. Principal genera: Lytoceras, Phylloceras (Fig. 258, D).—Trias to Cretaceous.

Fam. 10. Harpoceratidae.—Shell discoidal, compressed, margin keeled, surface with straight or arched ribs, aperture with lateral projections, suture with accessory lobes, aptychus in two pieces. Principal genera: Harpoceras, Oppelia, Lissoceras.—Jurassic to Cretaceous.

Fam. 11. Stephanoceratidae.—Shell discoidal, helicoid or straight, whorls sometimes disunited, surface often with bifurcating ribs, which are tubercled, aperture often with lateral projections, sutural line incised, aptychus in two pieces, sometimes united.

In the discoidal group, Stephanoceras is strongly ribbed, tubercled at the point of bifurcation, Cosmoceras has long lateral projections of the aperture when young, Perisphinctes has a large body-chamber and numerous smooth ribs. Other genera are Acanthoceras, Peltoceras, Aspidoceras, and Hoplites. Among the loosely whorled genera, Scaphites (Fig. 260, A) has the last whorl produced and bent back again in horse-shoe form, while the early whorls are concealed; Hamites, Hamulina, and Ptychoceras have a shell shaped like a single or double hook, the sides of which may or may not be united; Crioceras (Fig. 260, B) in form of whorls resembles a Spirula, Ancyloceras a Scaphites with the first whorls disunited. Macroscaphites (Fig. 259, B) is similar, but with the first whorls united and not concealed. Turrilites (Fig. 259, A) is turreted and sinistral, while Baculites is quite straight, with a long body-chamber.