Serial sections of skulls of four therapsid suborders, Gorgonopsia, Therocephalia, Anomodontia, and Cynodontia, have provided a basis for detailed studies of the cranial characters of reptiles which are approaching the mammalian threshold. Structures of the inner ear, the middle ear, the occipital region, and the basicranial axis are described in detail for each of the four suborders. Comparisons of the suborders are based on analyses of proportions of the parts of the brain case and the evolution of each part of the skull is traced. These analyses are used as a basis for studies of therapsid phylogeny and the origin of the mammals. The gorgonopsians are shown to be the probable ancestors of the cynodonts and the differentiation of the gorgonopsians, therocephalians, and anomodonts is placed in pre- Tapinocephalus times. Repeated independent development of suites of characters in the suborders is demonstrated. This leads to the conclusion that each suborder approached the mammalian threshold independently and that there are several possible sources of mammals among the therapsids. An analysis of mammalian phylogeny indicates several independent lines of mammalian development. Correlation of therapsid and mammalian phylogeny constitutes a basis for an hypothesis that three or more lines of mammals arose independently from different therapsid stocks. Tentative suggestions concerning the relationships of the therapsid and mammalian lines are considered briefly.