Rate constants for the reactions of muonium (Mu) (the ultralight isotope of the hydrogen atom) with H2 O2 in H2 O and D2 O2 in D2 O have been determined at various temperatures and pH (pD) values. The data are consistent with the three reactions: , , and the equivalent for the deuterated entities. A significant positive H/D isotope effect was found for the undissociated peroxide, while for the anions the effect was negligible or slightly in the opposite direction. In addition, for concentrated solutions of peroxide a study of the muon spin polarization as a function of applied transverse magnetic field yielded results consistent with the rate constants determined from the direct decay measurements, and indicated that the reaction products are diamagnetic, most likely MuH and MuOH, i. e., no muoniated radical products are formed. These results are potentially relevant for management of the radiolysis products in nuclear industry.