A new specimen of a sparassocynid didelphoid, consisting of a single skull, is described and analyzed. The specimen comes from the middle section of the Aisol Formation cropping out in Mendoza Province (Argentina) and constitutes the first marsupial hitherto described for the unit. The entire Aisol Formation was originally regarded as middle Miocene based on the fossil content. The discovery of new specimens, however, suggests that the stratigraphic level where the marsupial was found may have been deposited during the late Miocene (not older than Huayquerian times). The specimen studied here is identified as belonging to a new genus, Hesperocynus, of the family Sparassocynidae, Didelphoidea. A new combination is proposed for the already known species, H. dolgopolae (Reig 1958), previously recognized as a species of Thylatheridium Reig 1952. The new specimen from the Aisol Formation is assigned to the hypodigm of this taxon. The genus Hesperocynus encompasses small-sized carnivorous feeders as evidenced by their dental specializations and palate morphology; however, this taxon is more generalized than species of Sparassocynus, the other genus of the family. Sparassocynids have traditionally been considered the closest relatives of living didelphids. If this hypothesis is correct, then the sparassocynid clade has a long ghost lineage that covers at least 10 million years (as evidenced by the oldest known sparassocynid and didelphid remains). Sparassocynids and other didelphoids probably radiated after the global cooling event that occurred after the Eocene-Oligocene boundary.