Abstract The superoxide dismutase (SOD) activity of Cu,Zn-, Mn-, and Fe-SODs, and the SOD-like activity of ferricytochrome c, nitro blue tetrazolium (NBT), epinephrine, pyrogallol, l-ascorbic acid, and hydroxylamine, were investigated by the method of kinetic competition against superoxide radicals (O2−•) using ESR spectroscopy with a nitrone spin-trap 5,5-dimethyl-1-pyrroline N-oxide (DMPO). These activities depended on the pH and/or kind of the O2−• generating system used. A comparison of the results obtained for two O2−• generating systems of KO2 and hypoxanthine–xanthine oxidase showed that the effective pH in the former system was 1 or more higher than that in the latter. A new competition kinetic theory which includes a parameter of the stoichiometric ratio has been developed. Consequently, the profile of the non-stoichiometric competition reaction between DMPO and scavengers for O2−• was theoretically clarified.