Stout and long-tailed forms, with the tabulare cornua frequently much produced and pitted cranial bones; lateral lines well-developed; palate with teeth on palatines, vomers, premaxillæ, and maxillæ, the two latter elements bearing conical teeth and the others bearing short, stumpy cones, at least in one species; pineal foramen well forward; nostrils and orbits in the anterior part of skull; scapula peculiarly curved and pointed; other pectoral elements sculptured; neural spines and chevrons of caudal vertebræ much dilated at their extremities, and pectinated; no caudal ribs; vertebræ in one genus apparently capped with a sculptured plate as in _Zatrachys_; tail very long and tapering to a point, 50 to So caudal vertebræ; dorsal region short; limbs well developed, with clawed digits; carpus and tarsus cartilaginous; endochondrium well formed. There are 4 genera which constitute this family: _Urocordylus_, from the Coal Measures of Ireland; _Ceraterpeton_, from the Coal Measures of Ireland and England; _Diceratosaurus_, from the Coal Measures of Linton, Ohio; Eoserpeton, from the Coal Measures of Linton, Ohio. These may be distinguished by the following characters: I. Skull triangular, truncated behind, with rounded muzzle and aborted tabulare cornua, neural spines of caudal vertebræ long, slender, and expanded in a fan-like manner; tail with about 80 vertebræ; ventral scutes oat-like _Urocordylus._ II. Skull parabolic and of great width, with short cornua projecting from the supratemporal; tabulare cornua nearly twice as long; neural spines of caudal vertebræ low and wide; ventral scutes oblong; caudal vertebræ about 50 _Ceraterpeton._ III. Skull broad with obtuse snout, tabulare cornua absent, large, pointed posterior expansions from supratemporal, posterior table within the cornua truncate; vertebræ with an apical sculptured plate; caudal vertebræ numerous, over 75; ventral scutellæ bristle-like, arranged _en chevron_ _Diceratosaurus._ IV. Skull a broad oval, with large posterior projecting supratemporal horns, posterior table of skull between cornua truncate without the small lateral projection from the supratemporal, orbits a long oval, ribs long, curved and slender, tail unknown, possibly shorter than in other members of the family; it is restored as short in Journal of Geology, XVII, p. 77, fig. 20, 1909, but this is uncertain; the skull has all the characters of the family _Eoserpeton._