Oxygen equilibria in tench hemoglobin were analysed according to a three-state MWC model. In addition to the T and R states of the traditionally used two-state model, the three-state model introduces an additional state, the S state, when organic phosphates bind to the T-structure hemoglobin. Under conditions covering natural red cell pH values and nucleoside triphosphate-hemoglobin ratios, it was possible to closely fit experimental data to the three-state equation with constant values of the association constants KR, KT, and KS, and with only the allosteric constants L and M varying with effector conditions. Thus, in contrast to a twostate analysis of oxygen equilibria, the three-state analysis was consistent with the basic assumption of the MWC model, that heterotropic ligands only affect allosteric constants and not association constants. The temperature-dependence of the three-state parameter values showed that in the presence of nucleoside triphosphate the dominance of the S state over the T state was most pronounced at low temperatures. Furthermore, the numerical values of the enthalpy and entropy change of oxygenation were lower in the S state than in the T and R states, and the enthalpy and entropy change for the allosteric S→R transition were much larger than for the T→R transition. © 1990 Springer-Verlag.