It is known from fragmentary jaws and isolated teeth from a site in the early Barstovian, around 15–16 million years ago, of Nevada.

Together with other species from scattered localities in the United States, Japan, and Europe, Apeomyoides is classified in the subfamily Apeomyinae of the extinct rodent family Eomyidae.

In 1998, Oldřich Fejfar and colleagues reviewed Apeomys and identified a second, related genus Megapeomys, from the Early Miocene of Germany, the Czech Republic, and Japan.

[11] Apeomyoides savagei was described as a new genus and species by Kent Smith, Richard Cifelli, and Nicholas Czaplewski in 2006.

This tooth is characterized by four major cusps (protocone, paracone, hypocone, and metacone) and lophs or crests (protoloph, mesoloph, metaloph, and posteroloph), separated by synclines or valleys.

Like the upper teeth, they bear four cusps (metaconid, protoconid, entoconid, and hypoconid), four lophs (metalophid, mesolophid, hypolophid, and posterolophid) and three valleys.

[19] Syncline IV, which is located at the back of the tooth, between the hypolophid and posterolophid, is closed at the margins; this valley is open in Megapeomys bobwilsoni.

[20] On the mandible, the diastema is very large and the incisor is procumbent (projecting forward), which distinguishes Apeomyoides from most eomyids apart from Megapeomys.

[13] There is a masseteric scar (associated with the jaw muscles) from below the m1 forward to a point in front of p4, below the mental foramen, an opening in the jawbone.

[19] Apeomyoides savagei is from the Eastgate local fauna in the Monarch Mill Formation of Churchill County, Nevada.