The cathodic oxygen reduction has been investigated in 0.5 M H2SO4 and 0.1 M HClO4 on Pt single-crystal electrodes. The technique of the hanging meniscus rotating Pt single-crystal electrode (HMRE) was used. The kinetic parameters of O-2 reduction on Pt(lll), Pt(110) and Pt(100) were measured and the structural sensitivity and the influence of adsorbed species, especially adsorbed hydrogen, hydrogen sulphate ion and water, were examined. It was found that (1) the structure sensitivity of the O-2 reduction was not confirmed within the present experimental accuracy, (2) the "overshoot", appearing in the negative-going scan, resulted mainly from the O-2 diffusion transportation, and the adsorption of the hydrogen sulphate ion which was strongest on Pt(lll) retarded the O-2 reduction, (3) upd-H did not take part in this reaction, although the chemical H-2-O-2 reaction is rapid at Pt in gas phase, and (4) the sharp depression of the O-2 diffusion limiting current in a potential range of 0-0.1 V(RHE) was explained by a sharp decrease in the number of the vacant upd-H sites under the condition of almost full coverage. Thus, O-2 reduction is discussed as a process proceeding via adsorbed oxygen on the sites usually occupied by upd-H.