Actiobates

Cacops, is a genus of dissorophid temnospondyls from the Kungurian stage of the early Permian of the United States. Cacops is one of the few olsoniforms whose ontogeny is known. Cacops fossils were almost exclusively known from the Cacops Bone Bed of the Lower Permian Arroyo Formation of Texas for much of the 20th century. New material collected from the Dolese Brothers Quarry, near Richards Spur, Oklahoma in the past few decades has been recovered, painting a clearer picture of what the animal looked and acted like.

Dissorophidae is an extinct family of medium-sized, temnospondyl amphibians that flourished during the late Carboniferous and early Permian periods. The clade is known almost exclusively from North America.

Temnospondyli or temnospondyls is a diverse ancient order of small to giant tetrapods — often considered primitive amphibians — that flourished worldwide during the Carboniferous, Permian and Triassic periods, with fossils being found on every continent. A few species continued into the Jurassic and Early Cretaceous periods, but all had gone extinct by the Late Cretaceous. During about 210 million years of evolutionary history, they adapted to a wide range of habitats, including freshwater, terrestrial, and even coastal marine environments. Their life history is well understood, with fossils known from the larval stage, metamorphosis, and maturity. Most temnospondyls were semiaquatic, although some were almost fully terrestrial, returning to the water only to breed. These temnospondyls were some of the first vertebrates fully adapted to life on land. Although temnospondyls are amphibians, many had characteristics such as scales and armour-like bony plates that distinguish them from the modern soft-bodied lissamphibians.

Platyhystrix is an extinct temnospondyl amphibian with a distinctive sail along its back, similar to the unrelated synapsids, Dimetrodon and Edaphosaurus. It lived during the boundary between the latest Carboniferous and earliest Permian periods throughout what is now known as the Four Corners, Texas, and Kansas about 300 million years ago.

Acheloma is an extinct genus of temnospondyl that lived during the Early Permian. The type species is A. cumminsi.

Trematopidae is a family of dissorophoid temnospondyl spanning the late Carboniferous to the early Permian. Together with Dissorophidae, the family forms Olsoniformes, a clade comprising the medium-large terrestrial dissorophoids. Trematopids are known from numerous localities in North America, primarily in New Mexico, Oklahoma, and Texas, and from the Bromacker quarry in Germany.

Anconastes is an extinct genus of dissorophoid temnospondyl within the family Trematopidae. It is known from two specimens from the Late Carboniferous Cutler Formation of north-central New Mexico in the southwestern United States. The genus name derives from two Greek roots, ankos and nastes ("inhabitant"), which refers to the type locality of El Cobre Canyon where the specimens were found. The specific name is derived from the Latin word vesperus ("western"). The more complete specimen, the holotype, is a partial skull with articulated mandibles and a substantial amount of the postcranial skeleton. The less complete specimen, the paratype, consists only of the right margin of the skull with an articulated mandible.

Acroplous is an extinct genus of dvinosaurian Temnospondyli within the family Eobrachyopidae.

Broiliellus is an extinct genus of dissorophoid temnospondyl within the family Dissorophidae. Broiliellus is most closely related to the genus Dissorophus, and both have been placed in the subfamily Dissorophinae. Broiliellus is known from five species from the Early Permian: the type species is Broiliellus texensis, and the other species are Broiliellus brevis,Broiliellus olsoni, Broiliellus arroyoensis, and Broiliellus reiszi. An additional species, Broiliellus novomexicanus, which was originally named Aspidosaurus novomexicanus, is now thought to fall outside the genus as a member of the subfamily Eucacopinae.

Ecolsonia is an extinct genus of trematopid temnospondyl. Its phylogenetic position within Olsoniformes has been historically debated, but it is presently considered to be a trematopid.

Phonerpeton is an extinct genus of dissorophoid temnospondyl within the family Trematopidae that is known from the early Permian of Texas.

Fedexia is an extinct genus of carnivorous temnospondyl within the family Trematopidae. It lived 300 million years ago during the late Carboniferous period. It is estimated to have been 2 feet (0.61 m) long, and likely resembled a salamander. Fedexia is known from a single skull found in Moon Township, Pennsylvania. It is named after the shipping service FedEx, which owned the land where the holotype specimen was first found.

Olsoniformes is a clade of dissorophoid temnospondyls, including the families Dissorophidae and Trematopidae. Most members of the clade were highly adapted to a terrestrial lifestyle. The clade was named in 2008 and is defined as the least inclusive clade containing Dissorophus multicinctus and Acheloma cumminsi but not Amphibamus grandiceps, Micromelerpeton credneri, or Apateon pedestris. Olsoniforms share various features such as a stout and low ilium and a thin cultriform process. The earliest-branching olsoniform is Palodromeus bairdi, from the Late Carboniferous of Ohio.

Amphibamiformes is an unranked clade with Dissorophoidea created by Schoch (2018). It encompasses all of the taxa traditionally considered to be "amphibamids", branchiosaurids, and hypothetically lissamphibians under the traditional temnospondyl hypothesis of lissamphibian origins. These taxa are typically small-bodied dissorophoids and form the sister group to Olsoniformes, which comprises dissorophids and trematopids.