Of the ANOMALURIDÆ and HAPLODONTIDÆ no fossil remains are known. On the other hand, a North American fossil Rodent, described by Dr. Leidy under the name of _Ischyromys typus_, is regarded by Mr. Alston as the type of a distinct family, the _Ischyromyidæ_, nearly allied to the Sciuridæ, but also showing an affinity to the Beaver in some of its characters. The specimen described and figured by Dr. Leidy was obtained by Dr. Hayden from Miocene deposits in the “Bad Lands” of Wyoming. It was originally referred to the Sciuridæ, with which it agrees in its dentition, but is distinguished by its large infra-orbital opening, the presence of a sagittal crest, and the absence of post-orbital processes. The parietal region of the skull is much narrowed, and in this, as in the large size of the infra-orbital opening, _Ischyromys_ resembles the Musk Rat. Two other forms must be referred to here. Under the name of _Pseudotomus hians_, Professor Cope has described the remains of an animal which he believed to have been about the size of an Agouti, and originally thought to belong to the order Edentata. Subsequently he referred it to the Sciuridæ; but both Mr. Alston and Mr. Allen think that it may belong to the family Ischyromyidæ. In some respects the skull resembles that of _Arctomys_, but it has the same contraction between the orbits as _Ischyromys_ and _Fiber_. The incisor teeth are separated, and Professor Cope believes that the animal had only three molars on each side in each jaw. A still more doubtful member of the family is Professor Cope’s genus _Gymnoptychus_, which includes four species, all said to be from the “Tertiary of the Plains.” In this genus there are five molars above and four below on each side, as in _Ischyromys_ and the Sciuridæ; but these teeth show two crescents on the inner side in the upper, on the outer side in the lower jaw, and each crescent gives origin to a cross-ridge running to the opposite margin of the tooth.