Adelospondyli is an order of elongated, presumably aquatic, Carboniferous amphibians (sensu lato). They have a robust skull roofed with solid bone, and orbits located towards the front of the skull. The limbs were almost certainly absent, although some historical sources reported them to be present. Despite the likely absence of limbs, adelospondyls retained a large part of the bony shoulder girdle. Adelospondyls have been assigned to a variety of groups in the past. They have traditionally been seen as members of the subclass Lepospondyli, related to other unusual early tetrapods such as "microsaurs", "nectrideans", and aïstopods. Analyses such as Ruta & Coates (2007) have offered an alternate classification scheme, arguing that adelospondyls were actually far removed from other lepospondyls, instead being stem-tetrapod stegocephalians closely related to the family Colosteidae.
Most adelospondyls belong to the family Adelogyrinidae, and prior to 2003 the order and family were considered synonymous. In 2003, Ruta et al. assigned Acherontiscus to the order as the only known non-adelogyrinid member. As is the case in other lepospondyls, the teeth of adelospondyls did not have a maze-like internal structure like those of "labyrinthodonts", nor did adelospondyls possess enlarged fang-like teeth on the roof of the mouth. and a few "nectrideans" such as Scincosaurus and diplocaulids. Adelospondyls take this one step further. They possess only a single bone between the jaw joint and the skull roof. This bone is often believed to be a fusion between the tabular and the squamosal (termed a "tabular-squamosal" or "squamosotabular"),
Postcranial bones
Adelospondyls can also be characterized by their vertebrae compared to other lepospondyls. They were spool-shaped and high in number, with Acherontiscus having an estimated 64 vertebrae In fact, the name "adelospondyl" is Greek for "obscure vertebra", referencing both the rarity of adelospondyls and this trait. However, Watson also included Lysorophus as an adelospondyl rather than a lysorophian "microsaur", and other studies have shown that the absence of neurocentral fusion is very common among tetrapods, and therefore useless as a distinguishing feature.