This family is distinguished by the formula 3 1 4 3 -------, 3 1 4 3 by the incisors, canine and premolar 1 all being of subequal size, by all the teeth being brachydont, and by the crescents of the lower premolars and molars being modified. On these lower premolars and molars the anterior crescent is longer than the posterior, and the short posterior crescent on the exterior of the tooth; so that its anterior horn, instead of uniting with the posterior horn of the anterior crescent, comes in back to about the middle of the anterior crescent. Then the pillar, which in the other families is situated in the posterior crescent, is opposite the posterior horn of the posterior crescent. The small animals which represent this family are rare in the Deseado beds, much more abundant in the Casamayor. The family seems to have died out in the Deseado as no forms are referred to it in later epochs. We found no specimens belonging to the family; but to make this discussion complete, I will give a digest of Ameghino’s descriptions, with reproductions of such figures as he has given. All of the genera and species are based on very fragmentary material. The genera assigned to the family are _Trimerostephanos_, _Pleurocoelodon_, _Lophocoelus_ and _Henricofilholia_. =Trimerostephanos= Ameghino Trimerostephanos Amegh., 1895, Bol. Inst. Geog. Argen., t. 15, p. 646. Trimerostephanos Amegh., 1897, Bol. Inst. Geog. Argen., t. 18, p. 483. This genus is based on upper and lower teeth, and distinguished by the premolars and molars having a weak style on the anterior corner, and by the anterior lobe being considerably larger than the posterior. Four species have been described. =T. scabrus= Amegh., loc. cit. for genus. This is the type species, originally based on the third lower molar, to which was later added, upper premolar 4 and the molars, and lower molar 2. The following measurements are given: Upper premolar 4, length 15 mm., width 21 mm. Upper molar 2, length 31 mm. Upper molar 3, length 35 mm. Lower molar 2, length 20 mm. Lower molar 3, length 29 mm. [Illustration: Fig. 87. T. scabrus—natural size; _A_, upper premolar 4; _B_, lower molars 1 and 2.] =T. scalaris= Amegh., 1897, Bol. Inst. Geog. Argen., t. 18, p. 483, is based on lower pm. 2 to m. 2, a somewhat smaller species than the preceding, the series as given measuring 53 mm. [Illustration: Fig. 88. T. scalaris, premolar 2 to molar 2—natural size.] =T. angustus= Amegh., 1897, Bol. Inst. Geog. Argen., t. 18, p. 484. This species is described without a figure, as smaller than _T. scalaris_, pm. 2 to m. 2 being 59 mm. The mandible is also slenderer. =T. biconus= Amegh., 1897, Bol. Inst. Geog. Argen., t. 18. p. 484. This species is based on two lower premolars, said to be the same size as _T. angustus_, but with the pillar larger. =Pleurocoelodon= Ameghino