This family includes a large variety of forms from the formations from the Deseado up to the Mt. Hermosa, but all agree in having the first upper and the first two lower incisors enlarged into strong gnawing teeth; in the reduction or absence of in. 3, the canine, and premolar 1 of the upper and lower dentitions; in having the external face of the upper molars not inflexed; in lower molar 3 being three-lobed; and in the bulla being inflated and hollow. There are in the family two series of forms, at least, the one leading to the running _Hegetotherium_, the other to the hopping _Pachyrukhos_, and the very little known form _Phanophilus_ which may fit into one of the other series when better known. In the Deseado the following genera are assigned to the family. _Prohegetotherium_, like _Hegetotherium_, except that the last premolar and the molars have a vertical furrow near the external anterior margin. _Prosotherium_, 1 0 4 3 -------, 2 0 4 3 upper inc. 2 and 3 and lower inc. 3 vestigal, upper pms. not molariform, molars with a deep internal fold. _Propachyrucos_, -------, 3 1 4 3 lower jaw only, similar to _Pachyrukhos_ but have inc. 3, the canine, and pm. 1 present and only a little reduced. _Phanophilus_, upper molars only, but peculiar in having a strong external medial column. =Prohegetotherium= Ameghino Prohegetotherium Amegh., 1897, Bol. Inst. Geog. Argen., t. 18, p. 424. This little known genus is characterized by the upper molars having an external furrow near the anterior margin of the tooth. Otherwise it is similar to _Hegetotherium_. Ameghino described a species where the external surface of the bones was sculptured “like reptiles.” I do not see how, with the arrangement of the muscles usual to mammals, the sculpture could be similar to that of reptiles, and feel that this is due to conditions of weathering. We did not find this species, but did find a form which resembled it in general, but differed in being smaller and with the external furrow less developed. =Prohegetotherium sculptum= Ameghino P. sculptum Amegh., 1897, Bol. Inst. Geog. Argen., t. 18, p. 424. This species is characterized by the deep external furrow on the upper molars. The measure given is 34 mm. for the length of the three upper molars. =Prohegetotherium shumwayi= sp. nov. Founded on a portion of the right maxilla, carrying pm. 2 to 4 and m. 1, found on the Chico del Chubut, west of Puerto Visser, by Waldo Shumway. [Illustration: Fig. 29. H. Shumwayi—natural size.] The teeth are simple, with but a shallow external furrow near the anterior margin of the premolars and molar. A film of cement covers each tooth and extends to the top of the crown. The form is smaller than P. sculptum. MEASUREMENTS Upper premolar 3, length 6 mm., width 3¼ mm. Upper premolar 4, length 7 mm., width 3½ mm. Upper molar 1, length 7 mm., width 3½ mm. =Prosotherium= Ameghino