A new electrochemical oscillation (called oscillation B) appears, in addition to a reported one (called oscillation A), for reduction reactions on platinum electrodes in acid solutions containing hydrogen peroxide in case where the H2O2 concentration is made high. Also, oscillation A becomes more pronounced and more stable as the H2O2 concentration increases except the case of very high concentrations (greater than or equal to 1.1 M). Oscillation A appears in a narrow potential region just before hydrogen evolution, whereas oscillation B appears in a potential region of hydrogen evolution. Both oscillation A and B are strongly affected by the concentrations df H+ as well as H2O2, suggesting that they arise from the competition between the H2O2 and H+ reduction. It is concluded that the high and low current states for oscillation A correspond to the H2O2 reduction and almost no H2O2 reduction (nor hydrogen evolution), respectively, whereas the high and low current states for oscillation B correspond to the H2O2 reduction and hydrogen evolution, respectively. Mechanisms for sudden transitions between these states are discussed qualitatively.