The Order Adelospondyli, an isolated group of amphibians from the Carboniferous of the Edinburgh area, is redescribed and distinguished from other early tetrapods. Although systematics of genera and species is unsatisfactory, the group seems monophyletic, since as far as they are known, all conform to a single overall structural plan. There is an entire skull roof with a reduced complement of bones in an unique pattern, a highly characteristic marginal dentition, a massive hyoid apparatus, at least 70 holospondylous trunk vertebrae, and (like some other Lower Carboniferous tetrapods) a shoulder region with a heavy dermal girdle but no trace of ossified limbs or endochondral girdle. Adelogyrinids show no special affinity with other Palaeozoic amphibians: the vertebral characters in which they resemble microsaurs, lysorophids, aïstopods, and nectrideans may have evolved more than once among early tetrapods, and the shoulder girdle and neural arch characters shared with labyrinthodonts are probably primitive. The adelogyrinids thus illustrate the more general problems of establishing interrelationships among early tetrapods. Their way of life is discussed.