Spyroceras is pseudorthocerid

Pseudorthocerida

Pseudorthocerida are generally straight longiconic nautiloids with a subcentral to marginal cyrtochoanitic siphuncle composed of variably expanded segments which may contain internal deposits that may develop into a continuous parietal lining.. Cameral deposits are common and concentrated ventrally...

 genus from the Devonian of North America and Europe, defined by Hyatt in 1884. Pseudorthocerids are a kind of orthocertaoid

Orthoceratoidea

The Orthoceratoidea is a superorder , sometimes considered an infraclass or even a subclass, that comprizes nautiloid orders that have orthoconic to slightly cyrtoconic shells and central to subcentral siphuncles in which there may be internal deposits...

, a taxonomic group within the Nautiloidea. Specifically Spyroceras belongs to the pseudorthocerid family, Spyroceratidae.

Spyroceras was named for annulated orthocones with straight transverse sutures, transverse or slightly oblique surface annulations, and faintly cyrtoconic apeces. Surface ornamentation varies but longitudinal lirae are conspicuous from earliest stage. Siphuncle central or slightly offset ventrally, composed of expanded segments typical of the Pseudorthocerida. Cameral and siphonal deposits develop later than in most pseudorthocerids and are thus confined to the apical portion of the phragmocone.