Eutemnospondyli was named by German paleontologist Rainer R. Schoch in 2013.

He defined it as a stem-based taxon including all temnospondyls more closely related to Stereospondyli than to Edopoidea.

In his phylogenetic analysis, Eutemnospondyli included dendrerpetontids and a clade he referred to as Rhachitomi.

Rhachitomi is defined to include four major and well-supported clades of temnospondyls: Dvinosauria, Eryopidae, Stereospondyli and a clade formed by Zatracheidae and Dissorophoidea.

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