Using a general form of the directional mutation theory, this paper analyzes the effect of mutations in mutator genes on the G+C content of DNA, the frequency of substitution mutations, and evolutionary changes (cumulative mutations) under various degrees of selective constraints. Directional mutation theory predicts that when the mutational bias between A/T and G/C nucleotide pairs is equilibrated with the base composition of a neutral set of DNA nucleotides, the mutation frequency per gene will be much lower than the frequency immediately after the mutator mutation takes place. This prediction explains the wide variation of the DNA G+C content among unicellular organisms and possibly also the wide intragenomic heterogeneity of third codon positions for the genes of multicellular eukaryotes. The present analyses lead to several predictions that are not consistent with a number of the frequently held assumptions in the field of molecular evolution, including belief in a constant rate of evolution, symmetric branching of phylogenetic trees, the generality of higher mutation frequency for neutral sets of nucleotides, the notion that mutator mutations are generally deleterious because of their high mutation rates, and teleological explanations of DNA base composition.