A new species of rhynchodipterid lungfish, Soederberghia simpsoni, sp. nov., is described on the basis of a complete skull roof, and an incomplete but articulated head plus body, from the Upper Devonian Mandagery Sandstone near Canowindra, New South Wales (NSW, ^{Fig. 1A,}), Australia. It is compared with Soederberghia material from the upper part of the Catskill Formation, Pennsylvania ^{(Fig. 1B)}, and the Cloghnan Shale at Jemalong near Forbes, NSW, Australia. The Catskill and Cloghnan Shale material, consisting of two incomplete skull roofs, appears to be conspecific with the type species, Soederberghia groenlandica from the Famennian Remigolepis Series of Greenland. This is congruent with a recent suggestion that the Mandagery Sandstone is late Frasnian in age, whereas the upper Catskill Formation and Cloghnan Shale are Famennian. At the Famennian localities, Soederberghia is associated with tetrapods. Articulated postcranial material of Soederberghia, including the pectoral girdle, cranial and pleural ribs, unpaired fins and fin supports, is described for the first time. The presence of cranial ribs and a parasphenoid with a posterior stalk suggest that Soederberghia gulped air and probably inhabited a non-marine or shallow near-shore marine environment. The occurrence of Soederberghia groenlandica in the Famennian Old Red Sandstone of North America, Greenland and Australia thus furnishes evidence for contact or close proximity between Gondwana and Laurussia at this time, in conflict with some recent paleomagnetic data. The sister group of Soederberghia is Rhynchodipterus elginensis from the Famennian of Rosebrae near Elgin, Scotland; together they form the Family Rhynchodipteridae. Griphognathus, previously included in the Rhynchodipteridae, lacks a stalked parasphenoid and cranial ribs, and has a quite different dermal bone pattern from Soederberghia and Rhynchodipterus. We remove it from the group on these grounds, and interpret it as less crownward than the Rhynchodipteridae.