Despite the rapid mutational change that is typical of positive-strand RNA viruses, enzymes mediating the replication and expression of virus genomes contain arrays of conserved sequence motifs. Proteins with such motifs include RNA-dependent RNA polymerase, putative RNA helicase, chymotrypsin-like and papain-like proteases, and methyltransferases. The genes for these proteins form partially conserved modules in large subsets of viruses. A concept of the virus genome as a relatively evolutionarily stable "core" of housekeeping genes accompanied by a much more flexible "shell" consisting mostly of genes coding for virion components and various accessory proteins is discussed. Shuffling of the "shell" genes including genome reorganization and recombination between remote groups of viruses is considered to be one of the major factors of virus evolution. Multiple alignments for the conserved viral proteins were constructed and used to generate the respective phylogenetic trees. Based primarily on the tentative phylogeny for the RNA-dependent RNA polymerase, which is the only universally conserved protein of positive-strand RNA viruses, three large classes of viruses, each consisting of distinct smaller divisions, were delineated. A strong correlation was observed between this grouping and the tentative phylogenies for the other conserved proteins as well as the arrangement of genes encoding these proteins in the virus genome. A comparable correlation with the polymerase phylogeny was not found for genes encoding virion components or for genome expression strategies. It is surmised that several types of arrangement of the "shell" genes as well as basic mechanisms of expression could have evolved independently in different evolutionary lineages. The grouping revealed by phylogenetic analysis may provide the basis for revision of virus classification, and phylogenetic taxonomy of positive-strand RNA viruses is outlined. Some of the phylogenetically derived divisions of positive-strand RNA viruses also include double-stranded RNA viruses, indicating that in certain cases the type of genome nucleic acid may not be a reliable taxonomic criterion for viruses. Hypothetical evolutionary scenarios for positive-strand RNA viruses are proposed. It is hypothesized that all positive-strand RNA viruses and some related double-stranded RNA viruses could have evolved from a common ancestor virus that contained genes for RNA-dependent RNA polymerase, a chymotrypsin-related protease that also functioned as the capsid protein, and possibly an RNA helicase.