They have traditionally been seen as members of the subclass Lepospondyli, related to other unusual early tetrapods such as "microsaurs", "nectrideans", and aïstopods.
[1][2][3] 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.
Stem- and crown-tetrapods typically have three to four bones on each side of the skull in this region (from top to bottom): the tabular, supratemporal (and sometimes an adjacent intertemporal), and squamosal.
[1] Most of these vertebrae lack haemal spines, indicating that the primary elongation took place in the body rather than the tail.
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.
Adelospondyls retain the primitive condition of the two halves being completely fused, making their vertebrae unique among lepospondyls.
[1] Acherontiscus deviates from the norm of the subclass even more than other adelospondyls, as it possessed two separate bony components of the centra, rather than a single centrum (which is the case in adelogyrinids and other lepospondyls).
These two different components (the intercentrum at the front and pleurocentrum at the back) were nearly equal in size, similar to the vertebrae of embolomeres.
On the other hand, the bones of the endochondral shoulder girdle (i.e. the scapulae and coracoids), which supported the forelimbs, were lost along with the limbs.
Adelospondyls possessed a large bony hyoid apparatus, including gill-supporting bones such as hypobranchials and ceratobranchials.