Skull bones of Gosfordia truncata Woodward, 1891, from the Lower Triassic Hawkesbury Sandstone of New South Wales, Australia, are described for the first time. The skull roofing pattern suggests possible affinities between G. truncata and Paraceratodus germaini (Triassic, southwest Madagascar). A three-dimensional reconstruction of the skull of Ceratodus formosus Wade, 1935, based on the holotype, found in a Lower Triassic deposit at Brookvale in New South Wales, is included. This reconstruction indicates that this species is not closely related either to the recent Australian lungfish, Neoceratodus forsteri, or to the Triassic Ceratodus (Tellerodus) sturii from Nord Alpen in Austria, and it has no close affinities with G. truncata. A new genus, Ariguna, is therefore proposed to receive Ceratodus formosus Wade, 1935. Without associated tooth plate material, G. truncata and A. formosa cannot be defined more precisely.