A parsimony analysis of ‘higher’ temnospondyls (all temnospondyls descended from the common ancestor of Eryops and Parotosuchus) was performed using 37 terminal taxa and 121 osteological characters. Bremer support values for each internal node were calculated as a measure of clade strength. Additionally, the shortest trees that conformed to some alternative hypotheses were searched for. The following new taxa are established on the basis of the results: Euskelia (the clade containing the Eryopoidea and Dissorophoidea), Limnarchia (the clade containing Trimerorhachidae, Dvinosauroidea, Archegosauroidea and Stereospondyli), Dvinosauria (the clade containing Trimerorhachidae and Dvinosauroidea), Stereo-spondylomorpha (the clade containing Archegosauroidea and Stereospondyli), Capitosauria (the clade containing Lydekkerina and ‘capitosauroids’), and Trematosauria (the clade containing Trematosauroidea, Rhytidosteidae, Plagiosauroidea, Metoposauroidea and Brachyopoidea). The monophyly of the assemblage of Mesozoic families called the Stereospondyli by Romer is supported. The dominance of the Stereospondyli in the Mesozoic and its rarity in the Palaeozoic is discussed. It is suggested that the radiation of the diverse stereospondyl clades, the Capitosauria and Trematosauria, began in the Late Permian of Gondwana, in a ‘safe haven’ that was less severely affected by the Late Permian extinction event. It is further speculated that the ‘safe haven’ was located in Antarctica, or possibly Australia.