The dioxygen electroreduction reaction has been studied on nanosized metal (Cu(0), Ag(0))-ion-exchange matrix (macroporous sulfonated cation-exchange resin KU-23, sulfonated cation-exchange membrane MK-40) electrode materials. An increase in the half-wave potential of oxygen electroreduction from similar to 0.10 to 0.29 V on passing from the Na(+)- to the H(+)-form of the Me(0)-ion exchanger nanocomposite indicates the involvement of the H(+)-ion in the step of attachment of the first electron to the oxygen molecule O(2). The reaction of oxygen on the copper-KU-23 nanocomposite is accompanied by the appearance of an additional wave in the polarization curve of oxygen electroreduction in a neutral medium, which is associated with stabilization of hydrogen peroxide, a reaction intermediate, on nanosized copper. In the region of limiting current potentials, the rate-determining step of the array of electrochemical, chemical, and external- and internal-diffusion processes occurring during the electroreduction of oxygen is the external diffusion of O(2) molecules to the electrode surface.