The dermal skull roof of Acanthostega gunnari Jarvik is described in detail, giving new information on the anatomy, and new reconstructions of the skull in dorsal, lateral and occipital views, as well as sections through the skull at two points. The types of suture are compared with those of temnospondyls and discosauriscids, comparable animals in terms of habit and skull shape. The skull-bones of Acanthostega are much more closely integrated with each other than those of the two later groups. However, regions of relatively less firmly and more firmly sutured regions are comparable in position. This may be connected with having the lateral lines accommodated in tubes in Acanthostega rather than grooves, or some other property of the dermal bone in the later groups that reduced the need for stronger integration. The post-orbital region of the skull (skull table) is the most strongly integrated region, possibly connected with the need for attachment of occipital musculature. The skull table and dentition are the most labile of cranial features among Devonian tetrapods, whereas the snout, cheek, palate and infradentary regions remain conservative. These are for the most part the lateral-line-bearing regions of the skull. The specimens of Acanthostega found at one site on Stensiö Bjerg may form part of a year-group that had perhaps come together for spawning.