The neurocranium of Acanthostega gunnari is described from several specimens, and is the first full description of a Devonian tetrapod braincase. It is shown to resemble the osteolepiform Eusthenopteron in such features as the occipital arch and opisthotic region especially the crista parotica, post-temporal fossae, and grooves for the occipital artery dorsally. In contrast, it resembles other early tetrapods such as loxommatids and anthracosaurs in having a coossified sphenethmoid and otic region, in having large, bifaceted basipterygoid processes, in the incorporation of the stapedial footplate into the fenestra vestibuli, and in the elimination of the hyomandibular facets, lateral commissure and jugular canal. For soft tissue characters such as the course of the chorda tympani, the lateral head vein and the perilymphatic system, the primitive tetrapod condition is unknown and cannot be inferred from that in modern tetrapods. The primitive condition for the fenestra vestibuli is for the margins to be formed from a complex of sources; the otic capsule (proötic and opisthotic usually), the basioccipital (occipital arch origin) the basisphenoid (trabecular origin) and parasphenoid (dermal in origin). This condition is seen in most early tetrapods including all early amniote groups. The specialized condition in which it is confined to the otic capsule arose separately not only among frogs, mammals and turtles, but also, within diapsids, perhaps separately among lepidosauromorphs and archosauromorphs. The evolution of the otic region, including the hyomandibular/stapes cannot be understood from recent tetrapods alone, since primitive states are no longer represented among them. Other sarcopterygians and basal actinopterygians make better models than do modern tetrapods, for inferring the otic condition in early members of the group.