AbstractWeissia radians Hedwig is one of twelve names for Australasian mosses published in Hedwig'sSpecies Muscorum Frondosorumin 1801. While ten of the Hedwigian names (in their modern combinations) are used in twentieth-century Australasian floras,Weissia radianshas fallen into obscurity. Although no type specimen exists in the Hedwigian herbarium (G), a Joseph Banks collection from New Zealand is present in the Dawson Turner herbarium (BM). I believe the Banks material to be a portion of the original collection and here propose it as the lectotype ofW. radians. A combination based upon this basionym,Entosthodon radians(Hedw.) C. Müll., is the most appropriate name for this widespread Australasian species, which recent Australasian workers have misnamed asFunaria glabraTayl. The type of F. glabra Tayl., collected by James Drummond at Swan River in Western Australia, is referable toEntosthodon muehlenbergii(Turn.) Fife, a species widely distributed worldwide but rare in Australia and New Zealand. Synonymy is provided for these two species and their Australasian distributions are summarized. A lectotype is designated forEntosthodon claviformisC. Müll.&Hampe, a name that has been placed incorrectly in synonymy withFunaria glabraTayl., but which is here referred toEntosthodon apophysatus(Tayl.) Mitt. Evidence is presented that past selections of lectotypes for other Australasian Hedwigian names may have been inappropriate.