Abstract.•Linnaean binomial nomenclature is logically incompatible with the phylogenetic nomenclature of de Queiroz and Gauthier (1992, Annu. Rev. Ecol. Syst. 23:449-480): The former is based on the concept of genus, thus making this rank mandatory, while the latter is based on phylogenetic definitions and requires the abandonment of mandatory ranks. Thus, if species are to receive names under phylogenetic nomenclature, a different method must be devised to name them. Here, 13 methods for naming species in the context of phylogenetic nomenclature are contrasted with each other and with Linnaean binomials. A fundamental dichotomy among the proposed methods distinguishes those that retain the entire binomial of a preexisting species name from those that retain only the specific epithet. Other relevant issues include the stability, uniqueness, and ease of pronunciation of species names; their capacity to convey phylogenetic information; and the distinguishability of species names that are governed by a code of phylogenetic nomenclature both from clade names and from species names governed by the current codes. No method is ideal. Each has advantages and drawbacks, and preference for one option over another will be influenced by one's evaluation of the relative importance of the pros and cons for each. Moreover, sometimes the same feature is viewed as an advantage by some and a drawback by others. Nevertheless, all of the proposed methods for naming species in the context of phylogenetic nomenclature provide names that are more stable than Linnaean binomials. {Phylogenetic nomenclature; species names; binomial nomenclature.)