The rate of amino acid substitutions in the evolution of homologous proteins is remarkably constant. Furthermore, estimated rates of amino acid substitutions based on comparisons of the alpha hemoglobin chains of various mammals with that of the carp are about the same as those based on comparisons of the carp alpha and mammalian beta or the alpha and beta chains in mammals. These uniformities are regarded as evidence for the hypothesis that a majority of amino acid substitutions that occurred in these proteins are the result of random fixation of selectively neutral or nearly neutral mutations. TWO IMPLICATIONS OF THIS POSSIBILITY ARE DISCUSSED: (a) Random gene frequency drift is playing an important role in determining the genetic structure of biological populations and (b) genes in "living fossils" may be expected to have undergone as many DNA base (and therefore amino acid) substitutions as corresponding genes (proteins) in more rapidly evolving species.