The most well-known members of the group are
Sapheosaurus and
Kallimodon, and most
phylogenetic analyses on rhynchocephalians only study these two
genera as representatives of sapheosaurs. Although a few early phylogenies in the 1990s did not find that these two formed a natural clade, the relation between these two is now considered to be more stable, and has been found in practically every major analysis of rhynchocephalians since Apesteguía & Novas (2003). However, the relation between sapheosaurs as a whole and other rhynchocephalians is less clear. Although they are clearly members of the group
Sphenodontia like almost all other rhynchocephalians, the construction of their jaw joints means that they were unable to move their jaws in a front-to-back chewing movement. This excludes them from the clade of sphenodonts which are capable of such movement, the so-called "eupropalinal sphenodonts" such as the tuatara, (formally known as
Sphenodon), its close relatives, and the herbivorous
opisthodonts. They are also generally considered to be more derived (as in closer to
Sphenodon) than
clevosaurs and basal genera such as
Godavarisaurus and
Sphenocondor. The in-group relations of sphenodonts are inconsistent between analyses, so although sapheosaurs may be the
sister group of eupropalinal sphenodonts under some methodologies, other potentially more derived taxon include
Homoeosaurus,
Pamizinsaurus,
Ankylosphenodon, the
Sphenovipera+
Theretairus clade, and
pleurosaurs. A 2017 study utilizing both
parsimony and
bayesian analyses found some support for a clade including sapheosaurs,
Vadasaurus, and pleurosaurs. Although the bayesian analysis placed this clade in a large
polytomy with various other rhynchocephalian groups and genera, the parsimony analysis actually placed it among the eupropalinal sphenodonts. If this phylogeny is accurate, this would mean that an ancestor of this clade lost front-to-back chewing which was present in an even earlier ancestor, rather than never having it in the first place. A 2022 study found a clade containing pleurosaurs,
Vadasaurus, sapheosaurs
, Homoeosaurus, Kallimodon and
Leptosaurus, to the exclusion of other neosphenodontians like
Sphenodontidae. This clade was called Leptorhynchia. == Description ==