A model of evolutionary base substitutions that can incorporate different substitutional rates between the four bases and that takes into account unequal composition of bases in DNA sequences is proposed. Using this model, we derived formulae that enable us to estimate the evolutionary distances in terms of the number of nucleotide substitutions through comparative studies of nucleotide sequences. In order to check the validity of various formulae, Monte Carlo experiments were performed. These formulae were applied to analyze data on DNA sequences from diverse organisms. Particular attention was paid to problems concerning a globin pseudogene in the mouse and the time of its origin through duplication. We obtained a result suggesting that the evolutionary rates of substitution in the first and second codon positions of the pseudogene were roughly 10 times faster than those in the normal globin genes; whereas, the rate in the third position remained almost unchanged. Application of our formulae to histone genes H2B and H3 of the sea urchin showed that, in each of these genes, the rate in the third codon position is tremendously higher than that in the second position. All of these observations can easily and consistently be interpreted by the neutral theory of molecular evolution.