Agyrekocyathidae † (basis of record)
Alataucyathidae Zhuravleva, 1955 † (current name source)
Annulocyathidae † (basis of record)
Auliscocyathidae Debrenne & Zhuravlev, 1992 † (current name source)
Calyptocoscinidae Debrenne, 1964 † (current name source)
Carinacyathidae Krasnopeeva, 1953 † (current name source)
Chabakovicyathidae † (basis of record)
Chankcyathidae † accepted as Chankacyathidae Yakovlev, 1959 † (basis of record)
Claruscocoscinidae † accepted as Claruscoscinidae Debrenne & Zhuravlev, 1992 † (basis of record)
Erbocyathidae Volgdin & Zhuravleva, 1956 † (basis of record)
Eremitacyathidae Debrenne in Zamarreno & Debrenne, 1975 † (current name source)
Ethmocyathidae † (basis of record)
Fragilicyathidae Beljaeva in Beljaeva et al., 1975 † (current name source)
Fransuasaecyathidae Debrenne, 1964 † (current name source)
Geyericoscinidae † (basis of record)
Kasyriccyathidae † accepted as Kasyricyathidae Zhuravleva, 1961 † (basis of record)
Keriocyathidae Debrenne & Gangloff, 1990 † (current name source)
Konjuschkovicyathidae † (basis of record)
Kruseicnemididae Debrenne & Zhuravlev, 1990 † (current name source)
Loculicyathidae Zhuravleva, 1955 † (current name source)
Membranacyathidae † (basis of record)
Metacyathidae Bedford & Bedford, 1934 † (current name source)
Naimarkcyathidae † (basis of record)
Palaeoconulariidae † (basis of record)
Pycnoidocoscinidae † (basis of record)
Sakhacyathidae Debrenne & Zhuravlev, 1990 † (current name source)
Shiveligocyathidae † (basis of record)
Syringocnemidae † accepted as Syringocnemididae Taylor, 1910 † (basis of record)
Tabellarcyathidae † (basis of record)
Tchojacyathidae Debrenne & Zhuravlev, 1992 † (current name source)
Torosocyathidae † (basis of record)
Tubericyathidae † (basis of record)
Tubericyathidae † (current name source)
Tuvacnemididae Debrenne & Zhuravlev, 1990 † (current name source)
Tylocyathidae Zhuravlev, 1988 † (current name source)
Uralocyathellidae Zhuravleva, 1964 † (current name source)
Usloncyathidae Fonin in Vologdin & Folin, 1966 † (current name source)
Veronicacyathidae † (basis of record)