EOMYIDAE is an extinct family of rodents with a wide distribution in North America, Europe and Asia(1-3). Of the modern rodent groups, eomyids are most closely related to New World pocket mice (heteromyids) and pocket gophers (geomyids)(4). Eomyids occurred from the late Eocene through the Pliocene, spanning a time period of about 40 million years. From Europe alone, 11 genera and about 50 species have been recognized. The time of greatest diversity was the late Oligocene and early Miocene when eomyids dominated many small mammal faunas(1,5). Their fossil record, however, consists almost exclusively of teeth, with the postcranial skeleton being virtually unknown. Here we present a complete and extraordinarily well-preserved eomyid. Its soft body outline strongly suggests the existence of gliding membranes (Figs 1, 2). Thus eomyids are the fourth family of rodents (in addition to squirrels (Sciuridae), scaly-tailed flying squirrels (Anomaluridae), and dormice (Gliridae)) with representatives capable of gliding locomotion.