The paper presents a new method for inferring evolutionary trees using nucleotide sequence data. The method models the birth-death process as a prior distribution for phylogenies and branching times, while nucleotide substitution is modeled by a continuous-time Markov process. Parameters of both models are estimated using maximum likelihood. The posterior probabilities of different phylogenies are calculated, and the phylogeny with the highest posterior probability (MAP tree) is chosen as the best estimate of the evolutionary relationship among species. The posterior probability provides a measure of the reliability of the estimated phylogeny. The method is applied to two example data sets to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The results show that the best trees estimated by the new method are consistent with those from maximum likelihood analysis, but the posterior probabilities differ from bootstrap proportions. The method is also found to be insensitive to changes in the rate parameter of the branching process.The paper presents a new method for inferring evolutionary trees using nucleotide sequence data. The method models the birth-death process as a prior distribution for phylogenies and branching times, while nucleotide substitution is modeled by a continuous-time Markov process. Parameters of both models are estimated using maximum likelihood. The posterior probabilities of different phylogenies are calculated, and the phylogeny with the highest posterior probability (MAP tree) is chosen as the best estimate of the evolutionary relationship among species. The posterior probability provides a measure of the reliability of the estimated phylogeny. The method is applied to two example data sets to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The results show that the best trees estimated by the new method are consistent with those from maximum likelihood analysis, but the posterior probabilities differ from bootstrap proportions. The method is also found to be insensitive to changes in the rate parameter of the branching process.