The discoglossoid Frogs (Discoglossidae and Leiopelmatidae) are generally considered to be the most primitive of the living frogs. Previous authors have grouped them on the basis of common possession of a limited number of primitive features of little phylogenetic significance, leaving the question of intra-discoglossoid relationships uncertain. The present study is a re-examination df the supraspecific relationships in the superfamily using computer-aided cladistic analyses of a large set of osteological data - specifically 95 characters (153 binary characters) in 21 modern discoglossoid taxa. Where possible, characters are assigned a polarity, principally using urodeles as the outgroup. Evolutionary relationships are inferred from the congruence of cladograms generated from compatibility and parsimony analyses of the data set. In an introductory section, modern approaches to systematic analysis and classification are reviewed and a justification for the chosen method is provided. The concepts of natural taxa and natural classifications are discussed, criteria for hypothesizing character polarities and accounts of compatibility and parsimony analysis methods are given • •A. remarkable degree of congruence' between the cladograms produced from a Le Quesne compatibility analysis and a Wagner parsimony analysis is evident. Results suggest:- (a) The leiopelmatid genera Ascaphus and Leiopelma are a sister pair but are probably only weakly related. (b) The modern DiBcoglossidae is a monophyletic group in which Alytes is sister to Bombina + Barbourula + Discoglossus. (c)Discoglossus is sister to Bombina + Barbourula. (d)Bombina and Barbourula are a sister pair. (e)All the discoglossoid genera are monophyletic. (f)Bombina comprises two species groups: small (B. bombina - B variegata - B orientalis) and large species (B maxima and B microdeladigitora). Comparisons are made with previous work and an overview hypothesis of the historical zoogeography of the discoglossoid frogs is presented.