1. The primary events of haemoprotein reactions with molecular oxygen have been re-examined by placing special emphasis upon the reduction properties of dioxygen. 2. In the stepwise reduction of O2 to water via hydrogen peroxide, the addition of the first electron is an unfavourable, uphill process with the midpoint potential of -0.33 V, all the subsequent steps being downhill. This thermodynamic barrier to the first step is, therefore, a most crucial ridge located between the stabilization and the activation of dioxygen performed by haemoproteins. 3. If the proteins have a redox potential much higher than -0.33 V, molecular oxygen must bind to the proteins stably and reversibly. In Mb or Hb, however, the FeO2 centre is always subject to a nucleophilic attack of the water molecule or hydroxyl ion, which can enter the haem pocket from the surrounding solvent. These can cause irreversible oxidation of the FeO2 bonding to the ferric met-form with generation of the superoxide anion. 4. In cases of the oxygen activation, if haemoproteins have a redox potential lower than or close to -0.33 V, the first reduction of O2 to O2- would be a spontaneous process. Cytochrome P-450 provides such an example and can facilitate the subsequent addition of electrons that leads to the breaking of the O-O bond to yield the hydroxylating species. 5. As to the proteins whose redox potential is not facilitative and appreciably higher than -0.33 V, a bimetallic, concerted, two-equivalent reduction of the bound dioxygen to the peroxide level would be much more favoured without the intermediate formation of O2-. This is probably the case of cytochrome c oxidase for the reduction of O2 to water. 6. The redox potential diagrams thus visualize various aspects of the ways haemoproteins overcome their thermodynamic constraints and carry out their specific functions in the stabilization and the activation of molecular oxygen.