The allosteric properties of hemoglobins, especially their responses to ligands other than oxygen, vary widely in different classes of vertebrates. Knowing the stereochemistry of the cooperative effects in human hemoglobin, one can infer the stereochemical basis of these variations from the changes in amino acid sequence. The results indicate that the tertiary and quaternary structures of deoxy- and oxyhemoglobin have remained almost invariant during vertebrate evolution and that most of the amino acid replacements between species are functionally neutral. Adaptations leading to responses to new chemical stimuli have evolved by only a few (one to five) amino acid substitutions in key positions. Once such a response has become superfluous, it may be inactivated, not necessarily by a reversal of one of the original substitutions but by any other that happens to inhibit it.