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The current consensus view is that a higher hierarchical taxonomy of viruses cannot be established for two reasons. Firstly, viruses appear to be polyphyletic in origin, with several sets of viruses arising by different, independent routes at different times. Secondly, subsequent virus adaptation for survival in different host/vector combinations has involved the selective acquisition of additional genes by a process of cassette or modular evolution, with these additional gene modules coming from other viruses or host genetic material. Thus, depending on the gene product used for comparison, different phylogenetic relationships can be deduced. Further virus adaptation can arise by reassortment of segmented genomes, gene duplication, deletions, frameshift mutations, point mutations or de novo development of new gene products from existing, unused reading frames. The solution to the first objection is to place all viruses in a separate kingdom and assign the current viruses to several phyla that reflect these diverse origins. The solution to the second objection is to consider the core module of replication machinery as the major criterion on which to make the initial assignments to classes and orders. For RNA viruses, the major criterion is the sequence identity of the RNA-dependent RNA polymerase. Using this criterion, the positive strand RNA viruses can be assigned to five classes that correspond to the recently recognized supergroups of RNA viruses. These five classes contain four, three, three, three and one order(s) respectively. These fourteen orders contain 31 virus families (including 17 families of plant viruses) and 48 genera (including 30 genera of plant viruses). This approach confirms the separation of the alphaviruses and flaviviruses into two families, the Togaviridae and Flaviridae, but suggests that several other current taxonomic assignments, such as the pestiviruses, hepatitis C virus, rubiviruses, hepatitis E virus and arteriviruses, may be wrong. The coronaviruses and toroviruses appear to be distinct families in distinct orders, not distinct genera of the same family as currently classified. In addition, the luteoviruses are split into two families and apple chlorotic leaf spot virus appears not to be a closterovirus but a new genus of the Potexviridae. From an analysis of the polymerase dendrograms of the dsRNA viruses, it appears that they are not closely related to each other, but belong to four additional classes (Partitiviridae, Reoviridae, Birnaviridae and Cystoviridae) and one additional order (Totiviridae) of one of the classes of positive ssRNA viruses in the same subphylum as the positive strand RNA viruses.(ABSTRACT TRUNCATED AT 400 WORDS)