"Parastenopoceras", "Plummeroceras", and "Pselioceras" are from the Lower Permian; "Virgaloceras" is from the Upper Permian. The last three genera are from the Triassic, none having crossed from the Permian. "Grypoceras", given simply a Triassic, is like "Domatoceras" but tending to be more involute and to have more rounded ventral shoulders. "Menuthionautilus" from the Lower Triassic has a rapidly expanding, smooth involute shell with a deep dorsal impression, broadly convex flanks and rounded venter, suture with a shallow ventral lobe and siphuncle positioned against the venter. "Gryponautilus" from the Upper Triassic is broadly involute with a narrowly rounded, keel-like venter at maturity and shallow ventral and lateral lobes in the suture. All members of the Grypoceratidae have a ventral lobe with the exception of "Stenoporceras", "Parastenopoceras", and "Virgaloceras", which have a ventral saddle instead. The derivation of these three within the Grypoceratidae is uncertain. "Stenopoceras" or "Parastenopoceras" is the likely ancestor of the Syringonautilidae from the Triassic. The taxonomy of the Grypoceratidae in the Treatise on Invertebrate Paleontology is straightforward with no attempt to define subdivisions within the family. The taxonomy of the Centroceratina of Shimansky (1962) in Kummel (1964) is more involved. Shimansky first of all divided the Centroceratina into two superfamilies, the Tribolocerataceae with one family and the Centrocerataceae with six families. Among the Centroceratacea the Domatoceratidae and Grypoceratidae (sensu Shimansky) are equivalent to the Gypoceratidae of the Treatise. The Domatoceratidae which include forms with ventral lobes and ventral saddles extends from the Caboniferous barely into the Triassic. The Grypoceratidae of Shimansky contains the Triassic genera of Kummel's larger Grypoceraidae and are derived, probably in the Late Permian, from the more restricted Domatoceratidae.