We have reported [Bucci, E., Fronticelli, C, & Grycznski, Z. (1991) Biochemistry 30, 3195–3199] that in human and bovine hemoglobins the release of heat at the subsequent steps of oxygenation is not constant. This is especially evident in the binding of the third 02 molecule, which is an endothermic event. This phenomenon was attributed to peculiar conformations of the intermediates of oxygenation, not included in the fundamental R/T transition of the system. To test this hypothesis, we have explored the effect of conformational constraints on the thermodynamics of the intermediates of oxygenation. The assumption was that intramolecular constraints would stabilize the intermediates into conformations similar to the R and T forms reducing the variability of their enthalpies. We have analyzed the temperature dependence of the oxygen binding isotherms of human hemoglobin cross-linked either between the β82 or between the α99 lysines by bis(3,5-dibromosalicyl)fumarate. The measurements were performed at pH 9.0 in 0.1 M borate buffer in order to avoid thermal effects due to oxygen-linked binding of anions and protons. The data were analyzed singularly by local procedures and simultaneously using global procedures. The two cross-links had opposite effects. The cross-link between the β-subunits decreased while that between the α-subunits increased the endothermic behavior of the third step of oxygenation. Also, the cross-link between the β-subunits increased the fractional amount of the triligated species at intermediate stages of oxygenation, while that between the α-subunits decreased this quantity to hardly detectable values. These data are consistent with the hypothesis that the R/T transition in hemoglobin involves novel conformations not included in the R/T system. It is also speculated that the novel conformations of the intermediates of oxygenation is similar to the Y structure of hemoglobin Ypsilanti.