The relationships of the family are not far to seek. They fall in immediately with the Amphibamidæ and Hylonomidæ in being among the most reptile-like of the Paleozoic Amphibia. The group is, however, distinctly amphibian in the possession of 4 fingers, with the usual microsaurian phalangeal formula. =Genus DICERATOSAURUS Jaekel, 1903.= Jaekel, Neues Jahrbuch f. Mineral., Geol. u. Paleon., Bd. 1, p. 112, 1903. Moodie, Jour. Geol., XVII, pp. 63-69, figs. 13-15, 1909. Type: _Diceratosaurus punctolineatus_ Jaekel. Orbits in the anterior two-thirds of the axial skull length, nostrils near to the anterior end of the skull; pineal foramen in the center of the skull roof; skull provided with tabulate cornua and a broad backwardly directed process; quadrate angle does not project on the border of the skull; sculpture of the cranial elements impressed as radial grooves; 12 presacral vertebræ, 1 sacral with expanded neural spine which is sculptured at the top, with simple long, apparently separately ossified transverse processes; extremities small; foot with 5 digits; phalangeal formula 2-3-3-4-3. The most important differences between _Diceratosaurus_ and _Ceraterpeton_, the most nearly allied genus, is (in _Diceratosaurus_) in the more anterior position and small size of the orbits, the backward extension of the quadrate region, and the dorsal expansion of the vertebral spines. A further, and more important, difference between the genera is in the location of the backwardly directed processes from the skull. In Ceraterpeton they project backward from and are a portion of the tabulare element, while in Diceratosaurus the projection consists almost entirely of squamosal and supratemporal. =Diceratosaurus punctolineatus Cope.= Cope, Proc. Phila. Acad. Nat. Sci., 1875, p. 16. Cope, Geol. Surv. Ohio, II, pt. II, p. 372, pl. xli, fig. 4, 1875. Moodie, Bull. Am. Mus. Nat. Hist., XXVI, art. XXV, p. 356, pl. lxv, 1909. Type: Specimen No. 8606, American Museum of Natural History. Horizon and locality: Linton, Ohio, Coal Measures. The species was first described by Cope as _Ceraterpeton punctolineatum_ (122). It was redescribed on more abundant material (plate 19) by Jaekel (347), and the following is taken from the discussions of these two authors, checked by my own observations on the type specimen. This shows a portion of the skull, consisting of the squamosal and supratemporal with a projecting, convergent horn. The sculpturing on the skull is similar to that on the pectoral plates, of which there are three preserved (plate 14, fig. 4). The bones of the fore limbs are stout and short. The ribs are only slightly curved. The character of the vertebræ can not be ascertained. The sculpturing of the bones consists of radiating ridges, grooves, and pittings.