A discriminant analysis on the basis of the physicochemical properties of amino acid residues is developed to investigate the accumulation pattern of amino acid substitutions in a family of proteins. The application of this analysis to vertebrate hemoglobins reveals the following new results. (1) The major components of teleost fish and amphibian hemoglobins showing the Root effect are sharply discriminated from mammalian hemoglobins in several regions of the α and β chains, whereas shark, minor components of teleost fish and amphibian, reptile, and bird hemoglobins showing no Root effect exhibit a gradual change to mammalian hemoglobin in a straightforward way. This result suggests at least two lines of molecular evolution in vertebrate hemoglobins. (2) The nonadult hemoglobin chains are allocated to the latter line, i.e., tadpole, ξ, and π chains are similar to shark and trout I chains, and ∈ and γ chains are similar to some of the reptile chains. (3) In any case, most of the amino acid residues causing the discrimination are located near the sites that carry the amino acid residues conserved well throughout all classes of vertebrates, suggesting that modifications adapting to the respective living conditions or respiratory organs have taken place effectively near the amino acid residues essential for the manifestation of cooperative oxygen binding. (4) The amino acid residues at other sites are changed from one to another species even within the same class, showing a constant substitution rate as a whole. These amino acid substitutions may be nearly neutral, being under a weak functional constraint. The number of sites allowing such neutral substitutions is rather small, less than one-half of all the sites in the adult hemoglobins of bird and mammal, whereas it amounts to two-thirds in teleost fish hemoglobins.