Captorhinida is a doubly paraphyletic grouping of early reptile

Reptile

Reptiles are members of a class of air-breathing, ectothermic vertebrates which are characterized by laying shelled eggs , and having skin covered in scales and/or scutes. They are tetrapods, either having four limbs or being descended from four-limbed ancestors...

s. Robert L. Carroll

Robert L. Carroll

Robert Lynn Carroll is a vertebrate paleontologist who specialises in Paleozoic and Mesozoic amphibians and reptiles.Carroll was an only child and grew up on a farm near Lansing, Michigan...

 (1988) ranked it as an order in the subclass Anapsid

Anapsid

An anapsid is an amniote whose skull does not have openings near the temples.While "anapsid reptiles" or "anapsida" are traditionally spoken of as if they were a monophyletic group, it has been suggested that several groups of reptiles that had anapsid skulls may be only distantly related...

a, composed of the following suborders:

• Captorhinomorpha
  Captorhinomorpha
  Captorhinomorpha is a suborder of prehistoric reptiles which appeared in the Carboniferous period and became extinct after the Early Permian period....
  
  , containing families Protorothyrididae
  Protorothyrididae
  Protorothyrididae is a family of small, lizard-like reptiles. Their skulls did not have fenestrae, as is also true of modern turtles and tortoises. Protorothyridids lived from the Late Carboniferous to Early Permian periods, in what is now North America. Many genera of primitive reptiles were...
  
  , Captorhinidae
  Captorhinidae
  Captorhinidae is one of the earliest and most basal reptile families.-Description:...
  
  , Bolosauridae, Acleistorhinidae
  Acleistorhinidae
  Acleistorhinidae is a family of Early Permian-aged parareptiles. Presently, the clade consists of only two taxa, Colobomycter and Acleistorhinus, both collected from the Permian of Oklahoma. Sister taxa include Nyctiphruretidae and Sclerosauridae....
  
   and possibly also Batropetidae
• Procolophonia
  Procolophonia
  The Procolophonia are a suborder of herbivorous reptiles that lived from the Middle Permian till the end of the Triassic period. They were originally included as a suborder of the Cotylosauria but are now considered a clade of Parareptilia...
  
  , containing families Nyctiphruretidae, Procolophonidae and Sclerosauridae
• Pareiasauroidea, with families Rhipaeosauridae
  Rhipaeosauridae
  Rhipaeosauridae was a family of Procolophonids from the Permian time period.-Classification:Rhipaeosauridae was assigned to Cotylosauria by Tchudinov , to Pareiasauria by Olson , and to Pareiasauroidea by Carroll ....
  
   and Pareiasauridae
• Millerosauroidea, with a single family Millerettidae.

While they all share primitive features and resemble the ancestors of all modern reptiles, some of these families are more closely related to (or belong to) the clade Parareptilia

Parareptilia

Parareptilia is a subclass or clade of reptiles which is variously defined as an extinct group of primitive anapsids, or a more cladistically correct alternative to Anapsida...

, while others are further along the line leading to diapsid

Diapsid

Diapsids are a group of reptiles that developed two holes in each side of their skulls, about 300 million years ago during the late Carboniferous period. Living diapsids are extremely diverse, and include all crocodiles, lizards, snakes, and tuatara...

s. For this reason, the group is only used informally, if at all, by most modern paleontologists.