The genus contains small forms, with brachydont teeth. The upper molars consist of two laminae, separated by an internal and an external fold, and each lamina having, on the internal half, a deep furrow, which is but little shallower than the median fold; so that the outer side shows three furrows, folds, or pits, more or less completely separating four lobes; while on the inner side of the tooth there are but two lobes. On the lower teeth the external median fold is deep, while the internal median fold is shallower, usually appearing as a pit. Both the anterior and posterior laminae are subdivided by wide internal furrows which extend to the median line. These characters associate the genus with _Acaremys_ of the Santa Cruz, from which genus it is not easy to separate _Asteromys_; but as we know only the teeth from the Deseado beds, it is probable that, when the skull is found, larger differences will be recognized. _Asteromys_ appears to be the direct ancestor to _Acaremys_. The species are all tiny, the following three being distinguished by Ameghino. LENGTH OF LOWER MOLAR SERIES A. punctus (Bol. Inst. Geog. Argen., 1897, t. 18, p. 495) 12 mm. A. annectens (Bol. Acad. Nac. Cienc. Cordoba, 1902, t. 17, p. 37) 11 mm. A. prospicuus (Bol. Inst. Geog. Argen., 1897, t. 18, p. 495) each molar 1.6 to 1.8 mm. Of these three we found only the last. =Asteromys prospicuus= Ameghino A. prospicuus Amegh. loc. cit. above. [Illustration: Fig. 128. Right upper premolar 4—molar 3, × 4/1.] [Illustration: Fig. 129. Left lower molar 2, × 4/1.] The species is rare, only three specimens turning up in our collections. The upper molars are as described in the generic discussion, but premolar 4 is simpler than the molars, the posterior lamina being small and without any sort of furrow. In the upper molars the anterior lamina is larger than the posterior, and the anterior furrow wider than the posterior. The following measurements, with the figures, indicate the character of the species. Upper dentition, premolar 4 to molar 3 8.75 mm. Upper dentition, premolar 4, length 2. mm. Upper dentition, each molar, length 2.3 mm. Upper dentition, each molar, width 2. mm. Lower dentition, molar 2, length 2.75 mm. Lower dentition, molar 2, width 1.75 mm. =Eosteiromys= Ameghino Eosteiromys Amegh., 1902, Bol. Acad. Nac. Cienc., Cordoba, t. 17, p. 110.