It was established as a clade name by German paleontologist Rainer R. Schoch in 2013,[1] although the name had first been established in 1919 by British paleontologist D. M. S. Watson to encompass an evolutionary grade of temnospondyls leading to the group Stereospondyli.

American paleontologist Alfred Romer used the term in a similar sense, grouping most Permian and Triassic temnospondyls under Rhachitomi.

In rhachitomous vertebrae, the intercentrum is large and semicircular, while the pleurocentrum divided into two smaller paired elements.

Not all members of Rhachitomi have rhachitomous vertebrae; the largest subgroup, Stereospondyli, lacks pleurocentra.

Below is a cladogram from Schoch's analysis showing the placement of Rhachitomi within Temnospondyli:[1] Edopoidea "Dendrerpetontidae" Dvinosauria Zatracheidae Dissorophoidea Eryopidae Sclerocephalus Glanochthon Archegosaurus Australerpeton Rhinesuchidae Lydekkerina Capitosauria Trematosauria