This paper describes the inferential method, an approach for reconstructing protein and nucleotide sequences of ancestral species, starting from known, homologous, contemporary sequences. The method requires knowledge of the topology of the phylogenetic tree, whose nodes are the species to whom the reconstructed sequences belong. The method has been tested by computer simulation of speciation and nucleotide substitutions, starting from a single ancestral sequence, and by subsequent reconstruction of nodal sequences. Results have shown that reconstructions obtained by the inferential method are affected by limited error frequencies, which (1) are proportional to the squares of nucleotide substitution rates and of internodal distances, and (2) are little influenced by non-uniformity of transformation rates of nucleotides. Furthermore, good agreement of the results has been obtained by comparing protein-sequence reconstructions carried out with the inferential method with those obtained using the maximum parsimony method in two different cases: e.g., a reconstruction of simulated sequences and a reconstruction of mammalian ribonuclease sequences.