A method for molecular phylogeny construction is newly developed. The method, called the stepwise ancestral sequence method, estimates molecular phylogenetic trees and ancestral sequences simultaneously on the basis of parsimony and sequence homology. For simplicity the emphasis is placed more on parsimony than on sequence homology in the present study, though both are certainly important. Because parsimony alone will sometimes generate plural candidate trees, the method retains not one but five candidates from which one can then single out the final tree taking other criteria into account. The properties and performance of the method are then examined by simulating an evolving gene along a model phylogenetic tree. The estimated trees are found to lie in a narrow range of the parsimony criteria used in the present study. Thus, other criteria such as biological evidence and likelihood are necessary to single out the correct tree among them, with biological evidence taking precedence over any other criterion. The computer simulation also reveals that the method satisfactorily estimates both tree topology and ancestral sequences, at least for the evolutionary model used in the present study.