Perimecoceras is a nothoceratid

Nothoceratidae

Nothoceratidae is a family of nautiloid cephalopods in the orthoceratoid order Oncocerida in which shells are exogastrically or endogastrically breviconic, planospiral, or torticonic; often with a constricted or visored aperture; and a siphuncle commonly composed of concave segments and occupied by...

, nautilitoid order oncocerida, with a slowly expanding, compressed, cyrtoconic shell, known from the Upper Silurian

Silurian

The Silurian is a geologic period and system that extends from the end of the Ordovician Period, about 443.7 ± 1.5 Mya , to the beginning of the Devonian Period, about 416.0 ± 2.8 Mya . As with other geologic periods, the rock beds that define the period's start and end are well identified, but the...

 of central Europe.

Perimecoceras is similar in general form to the oncoceratid

Oncoceratidae

Oncoceratidae, a family in the Oncocerida established by Hyatt, 1884, which is characterized by generally compressed, cyrtoconic and breviconic shells with an exogastric curvature such that the ventral profile is convex or more so than dorsal, and in which the siphucle is generally empty and...

 genus Oonoceras

Oonoceras

Oonoceras is an extinct genus of nautiloid molluscs from the Silurian.-References:* Dinosaurs to Dodos: An Encyclopedia of Extinct Animals by Don Lessem and Jan Sovak...

from which it may have been derived, but differs in having a longer body chamber in proportion and in having concave segments to its siphuncle

Siphuncle

The siphuncle is a strand of tissue passing longitudinally through the shell of a cephalopod mollusk. Only cephalopods with chambered shells have siphuncles, such as the extinct ammonites and belemnites, and the living nautiluses, cuttlefish, and Spirula...

. It as also the most likely ancestral nothoceratid, probably giving rise to Blakeoceras

Blakeoceras

Blakeoceras is a nautiloid cephalopod from the Oncocerida family Nothoceratidae with a curved shell that lived in shallow seas from the Silurian to the middle Devonian in what has become Europe....

and other Nothoceratidae.

Perimecoceras probably lived on the sea floor, body chamber horizontal, phragmocone behind arched upward away from the bottom, using a combination of crawling and jet-swimming as it moved about.

-References-

• Sweet, W.C. 1964; Nautiloidea -Oncocerida; Treatise on Invertebrate Paleontology
  Treatise on Invertebrate Paleontology
  The Treatise on Invertebrate Paleontology published by the Geological Society of America and the University of Kansas Press, is a definitive multi-authored work of some 50 volumes, written by more than 300 paleontologists, and covering every phylum, class, order, family, and genus of fossil and...
  
  , Part K; Geological Society of America and University of Kansas press; Teichert and Moore (eds)
• Perimecoceras-Paleodb