_- Acrospiriferidae
- Adolfiidae
- Ambocoeliidae
- Brachythyrididae
- Choristitidae
- Crassumbidae
- Cyrtiidae
- Cyrtinopsidae
- Cyrtospiriferidae
- Delthyrididae
- Echinospiriferidae
- Elythidae
- Eudoxinidae
- Gerkispiridae
- Hedeinopsidae
- Hysterolitidae
- Ingelarellidae
- Kayseriidae
- Martiniidae
- Mucrospiriferidae
- Paeckelmanellidae
- Perissothyrididae
- Protozeugidae
- Reticulariidae
- Spinocyrtiidae
- Spiriferellidae
- Spiriferidae
- Spirigerellidae
- Strophopleuridae
- Syringothyridae
- Tenellodermidae
- Theodossiidae
- Trigonotretidae
- Ulbospiriferidae
- Verneuiliidae
- Xenomartiniidae