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 of 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.