Phylogenetic analysis of DNA sequences from primates, rodents, lagomorphs, artiodactyls, carnivores, and birds strongly suggests that the order Rodentia is an outgroup to the other four mammalian orders and that Artiodactyla and Carnivora belong to a superordinal clade. Further, there is strong evidence against the Glires concept, which unites Lagomorpha and Rodentia. The radiation among Lagomorpha, Primates, and Artiodactyla--Carnivora is very bush-like, but there is some evidence that Lagomorpha has branched off first. Thus, the branching sequence for these five orders of mammals seems to be Rodentia, Lagomorpha, Primates, Artiodactyla, and Carnivora. The branching date for Rodentia could be as early as 100 million years ago. The rate of nucleotide substitution in the rodent lineage is shown to be at least 1.5 times higher than those in the other four mammalian lineages.