Reptiles with two temporal openings in the skull are generally divided into two groups–the Lepidosauria (lizards, snakes, Sphenodon, ‘eosuchians’) and the Archosauria (crocodiles, thecodontians, dinosaurs, pterosaurs). Recent suggestions that these two are not sister-groups are shown to be unproven, whereas there is strong evidence that they form a monophyletic group, the Diapsida, on the basis of several synapomorphies of living and fossil forms. A cladistic analysis of skull and skeletal characters of all described Permo-Triassic diapsid reptiles suggests some significant rearrangements to commonly held views. The genus Petrolacosaurus is the sister-group of all later diapsids which fall into two large groups–the Archosauromorpha (Pterosauria, Rhynchosauria, Prolacertiformes, Archosauria) and the Lepidosauromorpha (Younginiformes, Sphenodontia, Squamata). The pterosaurs are not archosaurs, but they are the sister-group of all other archosauromorphs. There is no close relationship between rhynchosaurs and sphenodontids, nor between Prolacerta or Tanystropheus and lizards. The terms ‘Eosuchia’, ‘Rhynchocephalia’ and ‘Protorosauria’ have become too wide in application and they are not used. A cladistic classification of the Diapsida is given, as well as a phylogenetic tree which uses cladistic and stratigraphic data.