Archosaurian systematics is a constant state of flux, as various paleontological paradigms and sub-paradigms have came into and out of favour. Regarding the relationships of the basal archosaurs or Thecodontia, a number of different hypotheses have been offered over the last half century, any or none of which may be correct.
Until quite recently the Thecodontia (following the Linenan Evolutionary-Systematic approach) were considered a valid order divided into four suborders, the Proterosuchia, Phytosauria, the Aetosauria, and the Pseudosuchia. The Proterosuchia include various primitive ancestral types, the Phytosaurs are crocodile like forms, the Aetosaurs armoured creatures, remarkably like the armoured ornithischian dinosaurs, and the Pseudosuchia is a sort of catch-all or "waste-basket" category for everything that doesn't fit in any of the other suborders. This last group is also considered ancestral to dinosaurs, birds, and crocodiles.
Thecodontia - presents the old four suborder division. Some errors on this page - a few families presented under Pseudosuchia actually belong to the other suborders!
Although very similiar anatomically and clearly related to each other by common ancestry and many shared ancestral traits (plesiomorphies), the thecodonts are nowadays no longer considered a single taxon, but rather are divided along cladistic (ancestor-descendent) lines. Cladistics however offers no more objectivity than Evolutionary Systematics, as indicated by the rapidly changing cladistic paradigms, any (or all, or none) of which may be correct
One cladistic hypothesis has it that archosaurs (including thecodontia) can be classified according to whether they had crocodile-type or bird-type ankles. The Crocodile-type ankle ones are called Crocodylotarsi. This group includes the unfortunately named Pseudosuchia ("false crocodiles") and the Crocodylia. The bird-ankled types are called Ornithosuchia or Dinosauromorpha, and include the former "pseudosuchian" Ornithosuchidae, the Dinosaurs, and the birds. The Pterosaurs may also be included here. The Proterosuchia are too primitive to belong to either the crocodile or bird ankled group. Here are two cladograms (reproduced in Lars Juul's article "The phylogeny of basal archosaurs", Palaeont. Afr., 1994,) presenting this hypothesis.
J. Gauthier, 1986, "Saurischian
Monophyly and the origin of birds,"
in Padian K,. Ed., "The Origin of Birds and the Evolution of Flight", 1-55, 8, Memoirs, California Academy of Sciences, San Francisco
M.J. Benton and J.M. Clark 1988 "Archosaur phylogeny and the relationships of the Crocodilia" in MJ Benton (ed.), The Phylogeny and Classification of the Tetrapods 1:295-338. Oxford, The Systematics Association
The hypothesis presented in the above two cladograms was replaced by an alternative one when it was discovered (or decided) that the Ornithosuchus ankle is actually more like the Pseudosuchian one. This was argued in 1994 by Lars Juul, in The phylogeny of basal archosaurs. pp. 1-38. (see Lars Juul, 1994, "The phylogeny of basal archosaurs", Palaeont. Afr., 1994). This very technical paper that presents a subdivision of the early Archosauria following the cladistic method. This hypothesis again divides the Archosauria into two groups on the basis of their ankle structure: the Crurotarsi (all thecodontia apart from the Protosuchia) and the Ornithodira (dinosaurs, birds, lagosuchus and pterosaurs). The pseudosuchians are here presented as un unresolved trichotomy with with one group having prestosuchids and aetosaurs, a second with phytosaurs (Parasuchia) and a third, new, group - the Dromaeosuchia - which includes the Ornithosuchidae and the Paracrocodylomorpha (Crocodylomorpha plus Gracilisuchus and Poposaurids). The Ornithodira again is made up of pterosaurs, Lagosuchids and Dinosaurs. The paper is mentioned by Ralph Chapman at A few more.... Professor Paul Eric Olsen has a simplified version of teh cladogeram (and good introduction to the various reptilain types referred therein) on his page Great Triassic Assemblages Pt 1 - The Chinle and Newark. Here is the actual cladogram from the article:
Archosauriformes - has a cladogram and information on ankle structure and other features used in basal archosaurian classification, also argues that Ornithosuchidae may not belong in Crurotarsi - part of Jack Conrad's Vertebrate Phylogeny site
Archosauromorphs, Basal Archosaurs, Basal Crurotarsi - material by Toby White and yours truely - this page features a cladogram and information on basal archosaur relationships, also includes notes on different thecodontian taxa
The following table combines a number of these different interpretations:
a. Clade Archosauriformes
Family Euparkeriidae (or under Ornithosuchia)?
b. Clade Archosauria (consisting of Curotarsi and Ornithodira)