Rhynchorthoceras is a Middle Ordovician genus characterized by a rapidly expanded, weakly annulate orthocone

Orthocone

An orthocone is a usually long straight shell of a nautiloid cephalopod. During the 18th and 19th centuries, all shells of this type were named Orthoceras, but it is now known that many groups of nautiloids developed or retained this type of shell....

, like the orthoconic section of Ancistroceras

Ancistroceras

Ancistroceras is one of the two ancestral lituitids from the late Early Ordovician . The other being Holmiceras.The shell is weakly annulate, starts off with 1.5 to 2 contiguous or slightly separated whorls followed by a rapidly expanding orthocone with an apical angle of about 30 deg...

, but with only a curved, cyrtoconic apex instead of juvenile whorls.

Rhynchorthoceras is probably derived from Ancistroceras

Ancistroceras

Ancistroceras is one of the two ancestral lituitids from the late Early Ordovician . The other being Holmiceras.The shell is weakly annulate, starts off with 1.5 to 2 contiguous or slightly separated whorls followed by a rapidly expanding orthocone with an apical angle of about 30 deg...

 by a loss of the tarphycerid type apex, although it has been included with the orthocerid Sinoceratidae

Sinoceratidae

The Sinoceratidae is a family of orthoceroids, named for the genus Sinoceras, both by Shimizu and Obata 1935, and equivalent to the Michelinoceratinae Flower, 1945....

.

References

• Flower, R. H. 1950. A Classification of the Nautiloidia. Jour Paleontology, V.24, N.5, pp 604–616, Sept.
• Furnish & Glenister, 1964. Nautiloidea -Tarphycerida. 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, Mollusca 3 ...Nautiloidea