Five indigenous species of Pellaea in Australasia belong to section Platyloma. Their taxonomic history is outlined, morphological, cytological and genetic evidence for their recognition reviewed, and new morphological and chloroplast DNA-sequence data provided. Australian plants of P. falcata (R.Br.) Fée are diploid and have longer, narrower pinnae than do New Zealand plants previously referred to P. falcata, which are tetraploid. Evidence indicates that P. falcata does not occur in New Zealand, and that collections so-named are P. rotundifolia (G.Forst.) Hook. Chloroplast DNA sequences are uninformative in distinguishing Australian P. falcata from New Zealand P. rotundifolia, but show that Australian P. nana is distinct from both. Sequence data also show that Australian and New Zealand populations of P. calidirupium Brownsey & Lovis are closely related, and that Australian P. paradoxa (R.Br.) Hook. is distinct from other Australian species. Although P. falcata is diploid and P. rotundifolia tetraploid, P. calidirupium, P. nana (Hook.) Bostock and P. paradoxa each contain multiple ploidy levels. Diploid populations of Pellaea species are confined to Australia, and only tetraploids are known in New Zealand. Evolution of the group probably involved hybridisation, autoploidy, alloploidy, and possibly apomixis. Further investigation is required to resolve the status of populations from Mount Maroon, Queensland and the Kermadec Islands.