Revised diagnoses of the family Tarrasiidae and of Tarrasius (Visean of Scotland) and Paratarrasius (Namurian of North America) are presented. These are used in a phylogenetic analysis also comprising one theoretical outgroup, three sarcopterygians as part of the outgroup, and eleven Palaeozoic, Triassic, and Recent actinopterygians, and based on a matrix of 75 characters of head and body. The results are that: (1) Polypterus is the sister group of the other Actinopterygii (=Actinopteri); (2) the analysed Actinopteri are a monophyletic group (Palaeoniscimorpha); and (3) Tarrasiids are monophyletic and are the sister group of the other analysed Actinopteri. This scheme supports the most recent studies in indicating that Tarrasiidae are close to stem actinopterygians.