An accelerated method is suggested which enables an effective comparison to be made of amino acid (nucleotide) sequences of great length with due regard to a large number of possible gaps. The method consists in limiting the area of complete similarity charts, calculated in accordance with the algorithm suggested by Sankoff (1972), by a certain specially selected diagonal band. The application of the Monte-Carlo method permits a statistical evaluation to be made of the certainty of the similarity of the compared sequences and to choose on such a "comparison band", an optimum "correspondence path" which can readily be transformed into sequence alignment. Using this approach, prolactin and somatotropin families of sequences were found to be homologous at a high level of significance and their optimum alignment with two gaps has been suggested. In contrast, two regions of assumed partial gene duplication in beta-galactosidase sequence, suggested by Hood et al. (1978), were found not to be statistically significantly similar.