A description of the head, mandible, pectoral girdle, humerus, medial fins and their supports, and the dissociated vertebral column has been prepared for Onychodus jandemarrai n. sp. from the Gogo Formation (Frasnian) of Western Australia. This is the most completely known species of the genus. The feature influencing most of the head morphology is the retractable parasymphysial tusk whorls. Their presence has caused a reorganisation of the braincase, palate (including the loss of the vomers), and lateral displacement of the nasal capsules. The extensive mandibular articulation is in cartilage, and the mandibular symphysis is weak. This makes for a kinetic skull. There is a single submandibular on each side. The vertebral column is poorly ossified, consisting of intercentra which have no ventral contact, and pleurocentra. The neural arches have no longitudinal ligament, have unequal sides, and asymmetrical placing of the dorsal and ventral nerve root foramina. Each arch has an anterior surface that often attaches to the next anterior arch. The caudal fin is almost diphycercal; all the medial fins have strong support structures. An attempt is made to discuss the functional morphology of many features of the skeleton.

Stratigraphical and paleoecological evidence indicates that lungfkhes evolved in shallow marine conditions. Devonian genera had large gill chambers, and the details of bony supports of the gill arches of the Late Devonian Griphognathus whitei demonstrate that the arches were all functional. These data, together with an analysis of the body forms of the Devonian genera, indicate that they were dependent on gill (and possibly skin) respiration. The oldest known dipnoans, Uranolophus and Speonesydrion, are held to be representative of two lineages that can be recognized by their buccal and branchial features. One had a "rasping" dentition formed of denticles and marginal ridges that were continually shed and remodelled; the other had a "crushing" dentition characterized by the presence of variously modelled dentine masses that continued growth throughout the life of the animal.

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Attempts at understanding evolutionary relationships among Paleozoic Dipnoi (lungfish) using cladistic methodology have proved totally unsatisfactory (Miles 1977; Marshall 1987). We attempt to reconstruct the relationships between the better known genera using a method that involves the recognition of lineages based on evolving functional complexes, particularly those involved with food reduction and respiration. Within these broadly defined lineages, we have defined sub-lineages based on evolutionary patterns shown by structures that have been stratigraphically dated; such patterns are found inter alia in the roofing bones and the external dermal bones of the mandible. A number of new suborders and families are recognised; genera for which further morphological data are required before they can be assigned to a higher taxon are indicated; two generic synonyms are recognised.In appendices, short descriptions are given of two new genera—Pillararhynchus from the Gogo Formation (Upper Devonian) of Western Australia, and Sorbitorhynchus from the Emsian of Guangxi, China.