Sub-class I. _Monocyclica._--Crinoidea in which the base consists of BB only, the aboral prolongations of the chambered organ being interradial; new columnals are introduced at the extreme proximal end of the stem. Order 1. _Monocyclica Inadunata._--Monocyclica in which the dorsal cup is confined to the patina and occasional intercalated anals; such ambulacrals or interambulacrals as enter the tegmen remain supra-tegminal and not rigidly united. Families: Hybocrinidae, Stephanocrinidae, Heterocrinidae, Calceocrinidae, Pisocrinidae, Zophocrinidae, Haplocrinidae, Allagecrinidae, Symbathocrinidae, Belemnocrinidae, Plicatocrinidae, Hyocrinidae (recent), Saccocomidae. Order 2. _Adunata._--Monocyclica with dorsal cup primitively confined to the patina and an occasional single anal; tegmen solid; portions of the proximal brachials and their ambulacrals tend to be rigidly incorporated in the theca. Arms fork once to thrice, and bear pinnules on each or on every other brachial. BB fused to 3, 2 or 1. (Eucladocrinus and Acrocrinidae offer peculiar exceptions to this diagnosis.) Families: Platycrinidae, Hexacrinidae, Acrocrinidae. Order 3. _Monocyclica Camerata._--Monocyclica in which the first, and often the succeeding, orders of brachials are incorporated by interbrachials in the dorsal cup, while the corresponding ambulacrals are either incorporated in, or pressed below, the tegmen by interambulacrals; all thecal plates united by suture, somewhat loose in the earliest forms, but speedily becoming close, and producing a rigid theca; mouth and tegminal food-grooves closed; arms pinnulate. Sub-order i. _Melocrinoidea._--RR in contact all round; first brachial usually quadrangular. Families: Glyptocrinidae, Melocrinidae, Patelliocrinidae, Clonocrinidae, Eucalyptocrinidae, Dolatocrinidae. Sub-order ii. _Batocrinoidea._--RR separated by a heptagonal anal; first brachial usually quadrangular. Families: Tanaocrinidae, Xenocrinidae, Carpocrinidae, Barrandeocrinidae, Coelocrinidae, Batocrinidae, Periechocrinidae. Sub-order iii. _Actinocrinoidea._--RR separated by a hexagonal anal; first brachial usually hexagonal. Families: Actinocrinidae, Amphoracrinidae. Sub-class II. _Dicyclica._--Crinoidea in which the base consists of BB and IBB, the latter being liable to atrophy or fusion with the proximale, but the aboral prolongations of the chambered organ are always radial; new columnals may or may not be introduced at the proximal end of the stem.