The endoskeletal girdles, anocleithrum and paired fin supports of the porolepiform fish Glyptolepis (Osteichthyes: Sarcopterygii: Porolepiformes) are figured and described. The pectoral fin skeleton is known from the proximal part only and the pelvic fin skeleton is fragmentary, but the scapulocoracoid, anocleithrum and pelvic girdle can be reconstructed in their entirety. The anocleithrum is entirely subdermal. The pectoral fin skeleton in shown to be biserial, with a large number of axial mesomeres, whereas the pelvic fin contains fewer mesomeres and is strongly asymmetrical with very few postaxial radials. The scapulocoracoid is essentially similar to a reconstruction figured by Jarvik (1980), but has a more elongate glenoid; this has functional implications. The pelvic girdle consists of two separate halves as in Eusthenopteron, but differs from that genus in lacking dorsolateral rami. A brief survey of the evidence of paired fin structure in other porolepiform genera is carried out to establish whether the structures seen in Glyptolepis are likely to be representative for the Porolepiformes. A study of the morphology and muscle attachments of the paired fin skeletons indicates that the pattern of fin movement was significantly different from that in Neoceratodus. The fin supports and girdles of Glyptolepis are compared with those of other sarcopterygian groups as well as with actinopterygians, placoderms and sharks, in order to establish evolutionary polarities. Glyptolepis is shown to display a number of derived characters. The information gained from the comparison is used to construct a maximum parsimony cladogram, which places coelacanths as the sister group of porolepiforms + lungfishes, with the rhizodonts + tetrapods and osteolepiforms as successive sister groups of this clade. Characters of uncertain polarity are considered in the light of this cladogram. A comparison with recently published cladograms shows that none are completely compatible with the results from this study.