Nomenclature, taxonomy and species concepts of clonal (asexual) lineages have for a long time been hotly debated subjects. We argue that separating the 'asexuals' into different types, facilitates the discussion. In ancient asexuals, separate lineages have low intraspecific genetic and morphological variability and clear interspecific genetic and morphological gaps. Their taxonomy is thus (relatively) straightforward, species are conform to morphological, genetic and evolutionary species concepts. No special species concept for these taxa is necessary. In species with mixed reproduction, bisexual and asexual populations cluster amongst each other and form an inclusive species, with large intraspecific genetic and morphological variability. Accepting an inclusive approach, such species with mixed reproduction are again conform to morphological, genetic and evolutionary species concepts. Many problems remain, however,with the asexual spin-offs from species with sexual roots, be they advanced mutational lineages or interspecific hybrids. Congeneric lineages are often difficult to identifY unambiguously and, for several reasons, most of these clusters must be regarded as evolutionary species complexes for which a separate (theoretical) species concept (e.g. the agamospecies) must be invoked. Subspecies in clonal taxonomy should be avoided in all categories of asexuals, and this for different reasons. Possible exceptions are identifiable sib clones with special ecological preference.