Panperissodactyla

thumb|The white rhinoceros is the largest living perissodactyl

Litopterna (from "smooth heel") is an extinct order of South American native ungulates that lived from the Paleocene to the Pleistocene-Holocene around 62.5 million to 12,000 years ago (or possibly as late as 3,500 years ago), and were also present in West Antarctica during the Eocene. They represent the second most diverse group of South American ungulates after Notoungulata. It is divided into nine families, with Proterotheriidae and Macraucheniidae being the most diverse and last surviving families.

Phenacodontidae is an extinct family of large herbivorous mammals traditionally placed in the "wastebasket taxon" Condylarthra, which may instead represent early-stage perissodactyls. They lived from the late early Paleocene to early middle Eocene (about 60–50 million years ago) and their fossil remains have been found in North America and Europe. The only unequivocal Asian phenacodontid is Lophocion asiaticus.

thumb|Parsimony analyses consensus tree for phylogeny of anthracobunids from cladistic study by Cooper et al. (2014), showing them (near the bottom) placed within Perissodactyla next to [[Desmostylia.]]

Cambaytherium is an extinct genus of placental mammals in the family Cambaytheriidae. It existed during the early Eocene approximately 55 million years ago on the Indian subcontinent. Fossils of Cambaytherium are known exclusively from the Cambay Shale Formation in western India and comprise over 200 specimens, including skulls, teeth, and postcranial elements. The genus and family were first described scientifically in 2005. Initially, placement at the base of the odd-toed ungulates was preferred, though some researchers suggested affinity with elephants within Tethytheria. Recent systematic