The two-state model [Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88-118] postulates a single conformational change which, in the case of hemoglobin, has been related to the structural differences between deoxy and ligated hemoglobins [Perutz, M. F. (1979) Nature (London) 228, 726-739]. In its simplest form, the model does not represent satisfactorily either the equilibrium or the kinetics of the hemoglobin-oxygen reaction. The kinetic difficulty is with the rate of dissociation from the T-state, and may be met by assuming a wide difference in behavior between alpha- and beta-subunits. Experiments with Ni-Fe hybrids, however, show almost identical rates of combination with, and dissociation from, the two types of subunit, both of which develop R-like reactions as the pH is raised, the alpha-Fe-subunits at lower pH than the beta-Fe-subunits [Shibayama, N., Yonetani, T., Regan, R. M., and Gibson, Q. H. (1995) Biochemistry 34, 14658-14667]. The reactions of oxygen with hemoglobin A and the effect of pH upon them may be represented by assuming behavior of its subunits similar to that of the Ni-Fe hybrids. In such a scheme, alpha-alpha and beta-beta interactions become important elements in cooperativity, and more than two allosteric states are required, for reconsideration of the structural basis of cooperativity.