Paraphyletic species Telopea 6(4): 813-844. We present evidence, mainly from plants, that many recognised species and subspecies are paraphyletic. Whilst some cladists have argued that species are like other taxa, and should be monophyletic, it is clear that even cladists either implicitly or explicitly recognise nonmonophyletic species. Moreover, species concepts such as the phylogenetic species concept and the composite species concept predict non-monophyly of many species. Whenever a monophyletic species is circumscribed, it is possible that a paraphyletic or meta phyletic 'residual' species is simultaneously recognised. Furthermore, attempts to place all organisms in a monophyletic hlxon at every rank regress to the population level where monophyly is no longer applicable, leaving paraphyletic residuals. These groups of organisms can hardly be ignored, unless one wishes to define them out of existence (as in the monophyletic species concept). It has been argued that paraphyly is only an artifact of the Linnean system, which requires all organisms to be classified in certain ranks, e.g. species. However the phenonemon of regress shows that this is incorrect, because paraphyly is inherent in species. The solution to this conundrum is to recognise species as special taxa, which may be monophyletic or paraphyletic. (Higher taxa should always be monophyletic, and can be made so.) This requires the acceptance of a species concept that allows paraphyly, such as the phylogenetic species concept or the composite species concept. The monophyletic species concept, which does not allow paraphyly, is not acceptable. The special nature of species derives from their basal position in the phylogenetic system. Theoretically, the proportion of para phyletic and metaphyletic species may be 50% or higher. Empirical estimates range from 20% to 50%. Use of non-monophyletic species in historical applications such as biogeography is widespread but may not be invalid, depending upon the assumptions made.