Four new species of dipnoan fishes (lungfishes) are described from the Frasnian of Western Australia:Griphognathus whitei, Chirodipterus australis, C. paddyensisandHolodipterus gogoensis.These genera were originally set up for European species, and hitherto have not been known from the Southern Hemisphere. A detailed account of head structure is given for the first time in fossil dipnoans in a series of accounts of regional anatomy, each accompanied by a brief discussion. Interpretations in this part of the paper are based explicitly on the prior assumption that dipnoans are most closely related to crossopterygians, i.e. to choanates plus actinistians (coelacanths). The consequences of this assumption are exposed to criticism.The Gogo genera are divergently specialized.Griphognathushas an elongated snout and a primitive dentition of tooth‐ridges and buccal denticles.Chirodipterushas a short, blunt snout, a relatively short prepineal length and highly organized entopterygoid and prearticular tooth‐plates. The two Gogo species differ principally in tooth‐plate morphology.Holodipterushas a moderately elongated, broad snout and a dentition of knob‐like teeth and buccal denticles. All four Gogo dipnoans have an ossified neurocranium, meckelian cartilage, hyoid arch and gill‐skeleton, with both perichondral and endochondral bone. The quadrate is fused to the neurocranium by means of basal, ascending and otic processes, and there is a lateral occipital fissure contiguous with the reduced, posteriorly‐placed, ventral otic fissure. There are no visible sutures or ossification centres in the neurocranium.Griphognathusis exceptional in having at least one vertebral centrum included in the neurocranium and a pit for the attachment of the dorsal longitudinal ligament; the other forms have a large notochordal canal. The upper part of the otic region in all species bears lateral, dorsolateral, adlateral and median cristae, which raise the dermal skull‐roof above the surface of the neurocranium to leave wide passages for divisions of the adductor mandibulae muscles. The lateral face of the otic region bears an extensive hyomandibular facet which straddles the jugular canal. An adjacent, unossified area may be the site of Pinkus' organ (the spiracular sense organ). More ventrally, on the edge of the quadrate, there is a prominent bulge for the hyosuspensory ligament; and on the ventral surface of the neurocranium there is an articulation area for the first gill‐arch, which has previously been interpreted as the foramen for a hypothetical R. ventralis IX. The jugular groove is partly closed in by a prominent adotic process inGriphognathusand a small adotic eminence is present in the same position in other species. The cavum epiptericum, and the passages for all the major nerves and vessels in all the species can be interpreted by comparison with Recent dipnoans, particularlyNeoceratodus.However, there is no clear passage for the efferent pseudobranchial artery inGriphognathus;the posterior cerebral vein ofHolodipterusappears to have formed a network of vessels which passed out through several foramina in the otic region, rather than through the vagus foramen; and there is a network of canals draining into the orbit from the base of the cranium inChirodipterusandHolodipterus,otherwise known only inDipnorhynchus.There is an extensive supraotic cavity in the Gogo dipnoans, as inEusthenopteron,with an anterior paired and a posterior median division. This cavity housed extensive endolymphatic sacs. The paired endolymphatic duct opened on the surface of the neurocranium and extended up to the dermal skull‐roof in a groove on the dorsolateral crista. It may have opened to the outside in at least some specimens ofGriphognathus.The nasal cavities are open ventrally and there is a broad internasal septum as in other Devonian dipnoans; the anterior nasal opening notches the upper lip.Griphognathusis unique in having the nasal cavity partly floored, and in having a well‐defined posterior nasal opening between dermal bones of the palate.The dermal bones of the palate and ventral surface of the neurocranium include a parasphenoid with a long posterior stem and closed buccohypophysial canal, entopterygoid, dermopalatines and vomer. A posterior pit between the parasphenoid and neurocranium received the aortic ligament inGriphognathus.There are several dermopalatines inGriphognathusandHolodipterus,but only one inChirodipterus.There is also an ectopterygoid inGriphognathusand possibly inHolodipterus.The vomer is a median element inChirodipterusandHolodipterus;its presence inGriphognathusis unconfirmed. Thickenings on the dermal upper lip may indicate the inclusion of a premaxilla in the dermal snout. A vestigial maxilla may be present inGriphognathusin the form of tooth‐plates lying in the lateral wall of the nasal cavity. The lower jaw ramus is elongated inGriphognathusand there is a short retroarticular process; but the number of dermal bones is reduced from the primitive dipnoan number of seven, and the infradentary series is represented by only two main elements. The adductor pit is closed, indicating that the muscles inserted on the lateral face ot the angular. BothChirodipterusandHolodipterusretain the primitive number of dermal bones. The jaw ofChirodipterusis similar to that ofDipterus valenciennesibut it is relatively broader. That ofHolodipterusis exceptionally powerful. Both of these Gogo forms have a wide‐open adductor pit.Previous approaches to the interpretation of dermal bones of the skull‐roof and cheek of Devonian dipnoans are reviewed critically to diminish the risk of reaching false phylogenetic conclusions. The lateral‐lines and bone patterns ofGriphognathusandChirodipterusare normal for these sorts of dipnoans; those ofHolodipterusare less well known but present no unusual features. The operculo‐gular and submandibular series in all Gogo genera conform to the expected pattern:Chirodipterus australismay be exceptional in having only one subopercular bone. A fine dermal ornament is present inGriphognathusandHolodipterus,both of which lack cosmine on the head.Chirodipterus,however, is a cosmine‐bearing dipnoan, and this tissue displays all the qualities previously recorded in dipterids, including complete resorption of the outer layers of the dermal snout in some specimens. In all genera, the lateral‐lines open by small pores and there are richly developed rostral and symphysial tubuli.The hyoid and branchial arches are known in all species, but they are most completely preserved inGriphognathus.They answer closely to those ofNeoceratodus.There is a hyomandibula, accessory element (in one specimen only), large ceratohyal and hypohyal. The gill‐arches appear to lack pharyngobranchials; they clearly lack hypobranchials. The basi‐branchial series comprises a large anterior and a small posterior element, the first of which is co‐ossified with an elongated basihyal (“sublingual rod”) inGriphognathus.There is no sign of an ossified basihyal in the other forms. InGriphognathusalone, there is a urohyal which articulates with the basibranchial series, and paired anterior and posterior basibranchial tooth‐plates.The principal conclusions about the interrelationships of dipnoans are that previous systems are grossly unparsimonious, but that it is not possible to replace them with a satisfactory phylogenetic scheme. The most primitive species isDipnorhynchus sussmilchi.A series of derived characters can be recognized at more advanced levels, of which the most important involves the closure of the pineal foramen, changes in the dermal bone and lateral‐line patterns of the skull‐roof, modifications in the parasphenoid, and the origin and development of highly organized entopterygoid and prearticular tooth‐plates. These changes permit a rudimentary cladogram to be constructed, but this is, perforce, reminiscent of an anagenetic analysis. Many dipnoans cannot be classified in a phylogenetic scheme, includingChirodipterusandHolodipterus.Other conclusions are thatGriphognathusis a rhynchodipterid, and therefore most closids, in the accepted sense (includingDipterus valenciennesi, RhinodipterusandChirodipterus),probably form a grade group of unspecialized, cosmine‐bearing Devonian dipnoans; and thatNeoceratodusand lepidosirenids are more closely related to each other than they are toCeratodusand Triassic forms, or to gnathorhizids.The principal broader phylogenetic conclusions concern the interrelationships of sarcoptery‐gians, i.e. dipnoans, actinistians and choanates. The teleostome status of dipnoans is corroborated by a number of new observations, including the cranial fissure, supraotic cavity, urohyal, basibranchial tooth‐plates and aortic ligament. Sarcopterygians are assumed to be the collateral descendants (sister group) of actinopterygians, and Westoll's hypothesis that the intracranial joint is a primitive sarcopterygian character is upheld, against the author's previous opinion. Other sarcopterygian specializations are found in the general form of the otic and occipital region, the extensive hyomandibular facet(s) and the adotic process. The intracranial joint is secondarily absent in dipnoans, but these fishes are more closely related to choanates than they are to actinistians by several specializations, including the presence of cosmine, submandibular bones and a highly‐differentiated supraotic cavity. The first two of these specializations are also found in onychodontids, which may therefore be ch