No fossil LOPHIOMYIDÆ have yet been detected, but the great family MURIDÆ has left abundant evidence of its former existence. Species of the genera _Mus_, _Arvicola_, _Myodes_, and _Cricetus_, identical in many cases with those now living, have been obtained frequently in Post-Pliocene deposits and in bone-caves in Europe. Lemmings (_Myodes lemmus_ and _torquatus_) are recorded from English caves. The genus _Mus_ is also represented by several species in the Miocene deposits of France, and in the Sivalik beds investigated by Falconer and Cautley. The Miocene of Sansan has furnished a form which has been doubtfully regarded as a Gerbille, and named _Meriones Laurillardi_. In the same and other deposits of the same age in South-eastern France several species of an extinct genus (_Cricetodon_) have been obtained. Their dentition resembles that of the Hamster, but the first molars in both jaws have a tubercle less; the largest species (_C. sansaniensis_) rather exceeded the Hamster in size, while the smallest was less than a Mouse. Associated with some of these are two doubtful forms, _Decticus_ and _Elomys_, the latter considered by M. Aymard, its describer, to be allied to _Hydromys_. The American fossil Muridæ are for the most part either species of the genus _Hesperomys_, or nearly related to it. Twelve species of that genus were obtained by Dr. Lund from the Brazilian bone-caves, but of these eight were identified by him with species still existing. In North America two species of a nearly-allied genus (_Eumys_) have been obtained from Miocene deposits; and the bone-caves of Pennsylvania furnish the remains of a species of _Neotoma_ (_N. magister_), hardly distinguishable from the Florida Rat. A _Rhizomys_ from the Sivalik deposits of North-western India is the only recorded fossil representative of the SPALACIDÆ; and of the GEOMYIDÆ the only known species are a _Geomys_ from the Pliocene of Nebraska, nearly allied to, if not identical with, the living _G. bursarius_; and one from the “Tertiaries of the Plains,” described by Professor Cope as _Colotaxis cristatus_, which, however, has only three molars in the lower jaw. The DIPODIDÆ are still more scantily represented. A Jerboa described by M. Fischer from Post-Pliocene deposits, probably of Tartary, is very nearly allied to the living _Dipus platurus_, but has shorter toes and broader cannon-bones. The genus _Dipoïdes_, from the “Bohnerz” of Würtemberg, is founded on a single tooth, and its position in this family is very doubtful.