[1] When Marsh first named and described the tillodonts, he explained:[2] These animals are among the most remarkable yet discovered in American strata, and seem to combine characters of several distinct groups, viz: Carnivores, Ungulates, and Rodents.

In Tillotherium Marsh [=Trogosus], the type [specimen] of the order, the skull has the same general form as in the Bears, but its structure resembles that of Ungulates.

The molar teeth are of the ungulate type, the canines are small, and in each jaw there is a pair of large scalpriform incisors faced with enamel, and growing from persistent pulps, as in Rodents.When naming his new "pachyderm" species Trogosus castoridens ("beaver-toothed gnawing-hog"), Leidy added that it was a fossil "which would appear to have pertained to the stock from which diverged the Rhinoceros and Mastodon, the Peccary, and perhaps the Beaver.

[5] Azygonyx and Esthonyx from North America, Franchaius and Plesiesthonyx from Europe, and Basalina from Pakistan are all morphologically closely related but obviously geographically quite widespread.

This possible link between specimens from Pakistan and Europe with those from North America adds evidence to a faunal interchange between these continents during the early Eocene.