There are two species, both now extinct (E. Anderson 1984; Kurten 1968):
Holden (in Wilson and Reeder 1993) listed Hypnomys as a synonym of Eliomys. According to Kurten (1968), H. morphaeus was about as large as Myoxus and H. mahonensis was intermediate in size to Myoxus and Leitha Lydekker, 1896. Leitha was a giant dormouse about the size of a hamster, known from the middle and late Pleistocene of Malta and Sicily. Both species of Hypnomys survived the Pleistocene but subsequently disappeared. Extinction apparently came about 4,000-5,000 years ago and was associated with ecological disturbances caused by the spread of people and their domestic livestock across the Balearic Islands (P. S. Martin 1984; Vigne 1987).
Information taken from: Nowak, R.M. (Ed.). Walker's Mammals of the World. 6th Edition. The John Hopkins University Press. Baltimore and London, 1999.