Richly fossiliferous deposits have been found in the Ischigualasto region of Argentina in the last few years. The only known dicynodont from this area is the new genus Ischigualastia, of which a diagnosis and fully illustrated description are given. A specimen from Brazil, which had earlier been referred to the genus Stahleckeria as S. lenzii, is shown to be very similar to Ischigualastia, but not generically identical with it; this specimen is therefore placed in the new genus Barysoma. The only South American dicynodont which had previously been fully described is Stahleckeria, from Brazil. A diagnosis and fully illustrated description are now given of the complete skeleton of the genus Dinodontosaurus, also from Brazil. Earlier Brazilian material which had been referred to the African genus Dicynodon is shown to belong to Dinodontosaurus. A very large skull from the same deposits is identical with Dinodontosaurus, except that it has a much more massive snout and tusks, and a wider occiput. The dicynodonts are herbivorous, and may well have lived in herds; it is suggested that the massive skull may belong to the old male of such a herd of Dinodontosaurus, and it is therefore not given separate taxonomic status. The skull of Placerias, the only dicynodont known from North America, had previously been restored by Camp & Welles (1956) from the broken remains of about forty individuals. Comparison of the restored skull with that of Ischigualastia has suggested various modifications in the reconstruction, and illustrations of the new reconstruction are given. The relationships of the Triassic dicynodonts are discussed. It is suggested that, excluding the specialized genus Lystrosaurus, they show two main divergent adaptations, which are probably related to their mode of feeding. A pointed snout and high occiput is thought to characterize the family Kannemeyeriidae (which includes the forms Kannemeyeria, `Kannemeyeria' vanhoepeni, Sinokannemeyeria, Parakannemeyeria, Ischigualastia, Barysoma and Placerias). A blunt snout and wide occiput is thought to characterize the family Stahleckeriidae (which includes the genera Stahleckeria and Dinodontosaurus). A similar distinction is found today between the browsing black rhinoceros and the grazing white rhinoceros. The most primitive kannemeyeriids are found in the Lower Triassic of China, and these forms may also be ancestral to the stahleckeriids. The only other Triassic dicynodonts, Shansiodon and `Dicynodon' njalilus, may be placed in a separate family, the Shansiodontidae. All these Triassic genera have two features in common: the presence of a separately ossified olecranon process on the ulna, and a shortened interpterygoid vacuity. It is possible that this may indicate a common ancestry for them all, but no Upper Permian or Basal Triassic genera now known appear to be possible ancestors for them. The lack of any Middle Triassic vertebrate fauna in the northern hemisphere makes it very difficult to date the Argentinian and Brazilian faunas, which include gomphodont cynodonts, dicynodonts, rhynchosaurs, pseudosuchians and a few saurischians. It is not felt that the presence of rhynchosaurs necessarily indicates a Middle Triassic age, as the group is known from the mid-Norian of India. It is possible that the presence of several saurischians and of a pseudosuchian closely related to the German Norian genus Aetosaurus, may indicate a Carnian age for the Argentine fauna. The Brazilian fauna is somewhat dissimilar to that of Argentina and contains no genera in common with it; it may therefore be of earlier, Ladinian, age. The fauna of the Manda Beds of East Africa is similar in composition to that of Brazil, but contains no genera in common with it. It also lacks saurischians and includes a dicynodont, Kannemeyeria, that is otherwise typical of the Lower Triassic Cynognathus zone of South Africa. It may therefore be Anisian in age.