The electroreduction of O-2 at graphite electrodes on which the complex of Co(III) with the macrocyclic ligand C-meso-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane (hmc) is adsorbed proceeds in two steps that are well separated in potential. The first step consumes two electrons per molecule of adsorbed (hmcCo3+ to yield adsorbed (hmc)CoOOH2+. The second step involves the reduction of the adsorbed (hmc)CoOOH2+ to (hmcCo2+ + H2O2 followed by the reduction of O-2 to H2O2 catalyzed by the adsorbed (hmc)Co-3+/2+ complexes. A mechanistic scheme that accommodates the observed electrochemical responses is presented and tested by comparison with responses calculated by digital simulation methods. Differences between the electrochemical responses obtained with dissolved or adsorbed (hmcCo3+ are exposed and discussed. In addition, the behavior of the adsorbed (hmc)Co-3+/2+ system as it acts to electrocatalyze the reduction of O-2 is compared and contrasted with that exhibited by analogous adsorbed cobalt porphyrin electrocatalysts.