Anomaluroid rodents show interesting biogeographic and macroevolutionary patterns, although their fossil record is meager and knowledge of the natural history of extant members of the clade remains inadequate. Living anomaluroids (Anomaluridae) are confined to equatorial parts of western and central Africa, but the oldest known fossil anomaluroid (Pondaungimys) comes from the late middle Eocene of Myanmar. The first appearance of anomaluroids in the African fossil record coincides with the first appearances of hystricognathous rodents and anthropoid primates there. Both of the latter taxa are widely acknowledged to have originated in Asia, suggesting that anomaluroids may show a concordant biogeographic pattern. Here we describe two new taxa of African Paleogene anomaluroids from sites in the Sirt Basin of central Libya. These include a new Eocene species of the nementchamyid genus Kabirmys, which ranks among the oldest African anomaluroids recovered to date, and a new genus and species of Anomaluridae from the early Oligocene, which appears to be closely related to extant Zenkerella, the only living non-volant anomalurid. Phylogenetic analyses incorporating the new Libyan fossils suggest that anomaluroids are not specially related to Zegdoumyidae, which are the only African rodents known to antedate the first appearance of anomaluroids there. The evolution of gliding locomotion in Anomaluridae appears to conflict with traditional assessments of relationships among living anomalurid taxa. If the historically accepted division of Anomaluridae into Anomalurinae (extant and Miocene Anomalurus and Miocene Paranomalurus) and Zenkerellinae (extant and Miocene Zenkerella and extant Idiurus) is correct, then either gliding locomotion evolved independently in Anomalurinae and Idiurus or non-volant Zenkerella evolved from a gliding ancestor. Anatomical data related to gliding in Anomaluridae are more consistent with a non-traditional systematic arrangement, whereby non-volant Zenkerella is the sister group of a clade including both Anomalurus and Idiurus