Expressions that take into account the effects of thennodynamic non-ideality, described in terms of a high-order virial expansion, are derived for the concentration-dependence of the weight-average partition coefficient in exclusion chromatography of a single solute and of a solute undergoing reversible self-association. Comparison of the concentration-dependences predicted by those expressions with results obtained for bovine and human oxyhemoglobins on CPG-10-120 porous glass beads in 0.156 I phosphate-chloride buffer, pH 7.3, shows that neither oxyhemoglobin conforms with the concept of it being a single α2β2 entity with Stokes radius of 3.13 run, the experimental value. Previously published osmotic pressure and sedimentation equilibrium results are also shown to be inconsistent with this concept. On the other hand, both sets of exclusion chromatography results are consistent with the joint operation of thermodynamic non-ideality and reversible association of the α2α2 species. From the magnitude of the equilibrium constant, derived for either of two possible modes of association, it is calculated that only half of the oxyhemoglibin would be in the α2β2 states under conditions of oxygen saturation and a concentration of 320 g/liter, that pertaining in the red blood cell. The consequences of this association phenomenon are discussed in relation to the oxygen binding curves obtained by others in the presence and absence of 2,3-diphosphoglycerate (DPG). An explanation is provided of the observed dependence on hemoglobin concentration of oxygen-binding in the presence of DPG, and of the absence of such an effect in DPG-free solutions. It is concluded that the control of oxygen binding to hemoglobin in the physiological situation involves the joint operation of self-association and allosteric effects. © 1979.