Within Stereospondyli , Yates and Warren erected two major clades : Capitosauria and Trematosauria . Capitosaurs include large semiaquatic temnospondyls like Mastodonsaurus with flat heads and eyes near the back of the skull . Trematosaurs include a diversity of temnospondyls , including large marine trematosauroids , aquatic plagiosaurs , brachyopoids that survived into the Cretaceous , and metoposauroids with eyes near the front of their heads . In 2000 , paleontologists Rainer Schoch and Andrew Milner named a third major clade of stereospondyls , the Rhytidostea . This group included more primitive stereospondyls that could not be placed in either Capitosauria or Trematosauria , and included groups like Lydekkerinidae , Rhytidosteidae , and Brachyopoidea . While Capitosauria and Trematosauria are still widely used , Rhytidostea is not often supported as a true clade in recent analyses . Rhytidosteids and brachyopoids are now grouped with trematosaurians , but lydekkerinids are still considered to be a primitive family of stereospondyls .