linguistic:paraphrasing, information:extraction
Outer taxonomy

Traditionally, the odd-toed ungulates were classified with other mammals such as artiodactyls, hyraxes, elephants and other "ungulates". A close family relationship with hyraxes was suspected based on similarities in the construction of the ear and the course of the carotid artery.

Molecular genetic studies, however, have shown the ungulates to be polyphyletic, meaning that in some cases the similarities are the result of convergent evolution rather than common ancestry. Elephants and hyraxes are now considered to belong to Afrotheria, so are not closely related to the perissodactyls. These in turn are in the Laurasiatheria, a superorder that had its origin in the former supercontinent Laurasia. Molecular genetic findings suggest that the cloven Artiodactyla (containing the cetaceans as a deeply nested subclade) are the sister taxon of the Perissodactyla; together, the two groups form the Euungulata. More distant are the bats (Chiroptera) and Ferae (a common taxon of carnivorans, Carnivora, and pangolins, Pholidota). In a discredited alternative scenario, a close relationship exists between perissodactyls, carnivores, and bats, this assembly comprising the Pegasoferae.

According to studies published in March 2015, odd-toed ungulates are in a close family relationship with at least some of the so-called Meridiungulata, a very diverse group of mammals living from the Paleocene to the Pleistocene in South America, whose systematic unity is largely unexplained. Some of these were classified based on their paleogeographic distribution. However, a close relationship can be worked out to perissodactyls by protein sequencing and comparison with fossil collagen from remnants of phylogenetically young members of the Meridiungulata (specifically Macrauchenia from the Litopterna and Toxodon from the Notoungulata). Both kinship groups, the odd-toed ungulates and the Litopterna-Notoungulata, are now in the higher-level taxon of Panperissodactyla. This kinship group is included among the Euungulata, which also contains the even-toed ungulates and whales (Artiodactyla). The separation of the Litopterna-Notoungulata group from the perissodactyls probably took place before the Cretaceous–Paleogene extinction event. "Condylarths" can probably be considered the starting point for the development of the two groups, as they represent a heterogeneous group of primitive ungulates that mainly inhabited the northern hemisphere in the Paleogene.