The Mammalia are characterized by a limited degree of tooth replacement. This condition must have arisen from that typical of primitive reptiles, where the teeth are continually replaced throughout the animals' life. The therapsid reptiles include the ancestors of the mammals, and it is here that the origin of the mammalian mode of tooth succession is to be sought. The present paper describes an investigation of two groups of the more primitive therapsids, the Gorgonopsia and the Therocephalia, which lie close to the main line of synapsid evolution. The investigation involved the use of the recently developed methods of chemical preparation, along with X-ray examination of the material so prepared. In the Gorgonopsia and in the Therocephalia all the teeth were replaced at least once. Thus, none of their teeth can be equated with the molars of placental mammals, which are never replaced. Replacement of the incisors occurred at least twice and of the upper canines at least four times. Thus the condition in the mammals, where no tooth is replaced more than once, had not yet been achieved. Except in the upper canines there was no functional distichial replacement, each tooth being immediately replaced in function by the next generation of its own tooth family. The only sign of distichism is the tendency of the functional teeth to fall into two alternating groups in some cases, the members of each such group being replaced at about the same time. There are two alveoli in each maxilla for the upper canines. In the most primitive Therocephalia, and in the Gorgonopsia, there is only one functional canine on each side of the upper jaw, and this tooth is borne alternately by each of the pair of alveoli. Thus there is functional distichial replacement, since each canine is immediately replaced by a member of the tooth family of the other alveolus. This distichism is secondary, the ancestral Pelycosauria having two functional canines in each maxilla, each being immediately replaced by the next member of its own tooth family. Thus in the ultimate descendants of these theriodonts, the Mammalia, the deciduous and permanent teeth are almost certainly members of the same tooth family, with a possible exception in the case of the upper canines. The theory of Bolk (1922), that the two dentitions of the mammals are homologous with the alternating dentitions of primitive tetrapods, is unacceptable. The upper, and in one genus at least (Notosollasia) the lower, canines are shed by the erosion of the tooth through its cervix, the root being retained within the alveolus. The root is then penetrated by spongy bone and resorbed, the resorption starting at the cervix and proceeding along to its apex. This method of shedding the teeth appears to be unique. In the majority of the specimens the functional canine lies in the anterior alveolus, the posterior alveolus being filled with a plug of spongy bone, which often contains the remains of an old root undergoing resorption. In these examples there are no replacing canines, and replacement in the other teeth is limited or absent. This suggests that after a certain time in the animal's life tooth replacement ceased, the permanent upper canines being always borne by the anterior alveoli. In this limited tooth replacement the Gorgonopsia and the Therocephalia show an analogy with the mammals. The number of teeth is not fixed; for example, there may be seven incisors on one side and six on the other, or four cheek teeth on one side and five on the other. Thus tooth number is not a good taxonomic character.