Richard Owen's original definition of Perissodactyla included the modern members in addition to the now known to be unrelated Hyracoidea. The name Mesaxonia was resurrected by Martin S. Fischer in 1989 as a replacement for Perissodactyla.
Perissodactyla was initially defined by Richard Owen, including modern species along with the now-disconnected Hyracoidea. In 1989, Martin S. Fischer reintroduced Mesaxonia as an alternative classification for Perissodactyla.