There are at least two outstanding features that characterize the rate of evolution at the molecular level as compared with that at the phenotypic level. They are; (1) remarkable uniformity for each molecule, and (2) very high overall rate when extrapolated to the whole DNA content. The population dynamics for the rate of mutant substitution was developed, and it was shown that if mutant substitutions in the population are carried out mainly by natural selection, the rate of substitution is given byk = 4 N e s 1 v, whereN e is the effective population number,s 1 is the selective advantage of the mutants, andv is the mutation rate per gamete for such advantageous mutants (assuming that 4N e s 1 ≫ 1). On the other hand, if the substitutions are mainly carried out by random fixation of selectively neutral or nearly neutral mutants, we havek = v, wherev is the mutation rate per gamete for such mutants. Reasons were presented for the view that evolutionary change of amino acids in proteins has been mainly caused by random fixation of neutral mutants rather than by natural selection. It was concluded that if this view is correct, we should expect that genes of “living fossils” have undergone almost as many DNA base replacements as the corresponding genes of more rapidly evolving species.