Hercoglossidae was established by Spath in 1927 for smooth, involute nautiloids characterized by a suture with differentiated elements, known from the Upper Jurassic to the Oligocene. Hercoglossids make up part of the Nautilid

Nautilida

The Nautilida constitute a large and diverse order of generally coiled nautiloid cephalopods that began in the mid Paleozoic and continues to the present with a single family, the Nautilidae which includes two genera, Nautilus and Allonautilus, with six species...

 superfamily Nautilaceae. (Kummel 1964)

Four genera are described in the Treatise (Kummel 1964). They are Hercoglossa, Aturoidea, Cimonia, and Deltoidonatilus. All have a whorl section that is generally rounded, except for Deltoidonatilus where in it is triangular in outline. Sutural completity increases from Cimonia to Hercoglossa and to Aturoidea. The suture in Deltoidonautilus is like than in Hercoglossa. (ibid)

Cimonea, which intergades with Eutrephoceras, is the earliest and makes its first appearance in the Upper Jurassic

Jurassic

The Jurassic is a geologic period and system that extends from about Mya to  Mya, that is, from the end of the Triassic to the beginning of the Cretaceous. The Jurassic constitutes the middle period of the Mesozoic era, also known as the age of reptiles. The start of the period is marked by...

. Eutrephoceras is assigned to the Nautilidae which includes Nautilus

Nautilus

Nautilus is the common name of marine creatures of cephalopod family Nautilidae, the sole extant family of the superfamily Nautilaceae and of its smaller but near equal suborder, Nautilina. It comprises six living species in two genera, the type of which is the genus Nautilus...

. Hercoglassa, which is derived from Cimonia, first appears in the Lower Cretaceous and is followed stratigraphically by Aturoidea and Delltoidonautilus which first appear in the Upper Cretaceus. Aturoidea is the source for Aturia, to which it gave rise in the Paleocene. (ibid)

References

• Kummel, B 1964. Nautilioidea - Nautilida, in the Treatise on Invertebrate Paleontology, Part K Nautiloidea, Geological Society of America and University of Kansas press. (K455-K457)