A formal mathematical analysis of the substitution process in nucleotide sequence evolution was done in terms of the Markov process. By using matrix algebra theory, the theoretical foundation of Barry and Hartigan's (Stat. Sci. 2:191-210, 1987) and Lanave et al.'s (J. Mol. Evol. 20:86-93, 1984) methods was provided. Extensive computer simulation was used to compare the accuracy and effectiveness of various methods for estimating the evolutionary distance between two nucleotide sequences. It was shown that the multiparameter methods of Lanave et al.'s (J. Mol. Evol. 20:86-93, 1984), Gojobori et al.'s (J. Mol. Evol. 18:414-422, 1982), and Barry and Hartigan's (Stat. Sci. 2:191-210, 1987) are preferable to others for the purpose of phylogenetic analysis when the sequences are long. However, when sequences are short and the evolutionary distance is large, Tajima and Nei's (Mol. Biol. Evol. 1:269-285, 1984) method is superior to others.