We present a further application of the stochastic model previously described (Lanave et al., 1984, 1985) for measuring the nucleotide substitution rate in the mammalian evolution of the mitochondrial DNA (mtDNA). The applicability of this method depends on the validity of "stationarity conditions" (equal nucleotide frequencies at first, second and third silent codon positions in homologous protein coding genes). In the comparison of homologous sequences satisfying the stationarity condition at the silent sites, only the four codon families (quartets) for which both transitions and transversions are silent at the third position are considered here. This has allowed us to estimate the transition and transversion rates for any pair of species. We have analyzed the third silent codon position of the triplet rat-mouse-cow, of a series of slightly divergent primates and of two Drosophila species. In terms of two external dating input we have then determined the phylogenetic trees for rat, mouse, and cow as well as for a number of primates including man. The phylogenetic tree that we have derived for the triplet rat, mouse and cow agrees with that we had previously determined by analyzing the first, second and third silent codon positions (in both duets and quartets) of mt genes (Lanave et al., 1985). For primates our method leads to the following branching order from the oldest to the most recent: Gibbon, Orangutan, Gorilla, Chimpanzee and Man. In absolute time, fixing the distance Chimpanzee-Man as 5 million years (Myr) we estimate the dating of the divergence nodes as: Gorilla 7 Myr; Orangutan 16 Myr; Gibbon 20 Myr. In all cases analyzed, the transition rate has been found to be substantially higher than the transversion rate. Moreover we have found that the transition/transversion ratio is different in the various lineages. We suggest that this fact is probably related to the nucleotide frequencies at the third silent codon position.