In cytochrome c oxidase, oxido-reductions of heme a/Cu(A) and heme a3/Cu(B) are cooperatively linked to proton transfer at acid/base groups in the enzyme. H+/e- cooperative linkage at Fe(a3)/Cu(B) is envisaged to be involved in proton pump mechanisms confined to the binuclear center. Models have also been proposed which involve a role in proton pumping of cooperative H+/e- linkage at heme a (and Cu(A)). Observations will be presented on: (i) proton consumption in the reduction of molecular oxygen to H2O in soluble bovine heart cytochrome c oxidase; (ii) proton release/uptake associated with anaerobic oxidation/reduction of heme a/Cu(A) and heme a3/Cu(B) in the soluble oxidase; (iii) H+ release in the external phase (i.e. H+ pumping) associated with the oxidative (R-->O transition), reductive (O-->R transition) and a full catalytic cycle (R-->O-->R transition) of membrane-reconstituted cytochrome c oxidase. A model is presented in which cooperative H+/e- linkage at heme a/Cu(A) and heme a3/Cu(B) with acid/base clusters, C1 and C2 respectively, and protonmotive steps of the reduction of O2 to water are involved in proton pumping.