A data matrix comprising 96 selected wing venation characters from each of 15 fossil and 32 extant spp. was analysed using cladistic parsimony algorithms. The results indicate that suborder Anisoptera is a natural (i.e. monophylelic) grouping, but that both Anisozygoptera and Zygoptera are paraphyletic. Within the extant order, coenagrionoid and lestoid families occupy the basal branches of the phylogenetic tree. Next comes Calopterygoidea as a monophyletic group, then Amphipterygidae, then Anisozygoptera, and finally Anisoptera as a monophyletic group. The Australian endemic species Hemiphlebia mirabilis Selys is indicated as sister to a clade comprising the whole remainder of the modem order, plus the Permian suborders Protozygoptera and Archizygoptera and the Triassic suborder Triadophlebiomorpha. If this phylogenetic estimate is correct, the conservation value of H. mirabilis is far greater than its current taxonomic status as a monotypic superfamily would suggest.