Ab initio molecular orbital methods have been used to study the oxidation of ammonia, dihydrogen sulfide, and dimethyl sulfide by hydrogen peroxide and methyl hydroperoxide. Geometries of reactants, complexes, transition states, and products were fully optimized at the MP2/6-31G* level, and relative energies were computed at the MP4/6-31G*//MP2/6-31G* level. Without protic solvent catalysis, a 1,2-hydrogen shift is needed before oxygen transfer from H2O2 takes place and the barriers are much too high (ca. 50 kcal/mol). One or two molecules of protic solvent reduce these barriers by ca. 10 kcal/mol. In the absence of protic solvents, the hydroperoxide itself can act as a general acid catalyst, leading to second-order kinetics in H2O2 (in agreement with experiment). An increase in pK(a) of the general acid catalyst results in a decrease in activation energy for oxygen atom transfer from hydrogen peroxide. The mechanism for oxidation of sulfur is similar to that of oxidation of NH3, and methyl substitution at sulfur results in a modest stabilization of the transition state. For methyl hydroperoxide oxidation of ammonia, an ionic pathway is slightly lower in energy and involves a proton shift occurring after transfer of HO+. In agreement with experiment, protonation by strong acids has a much larger effect on the barrier than catalysis by weak acids such as H2O, H2O2, and NH3. However, the calculations show that under acidic conditions protonation occurs at the nucleophile rather than the peroxide, thereby greatly diminishing the catalytic effect. Nevertheless, all of these oxidation reactions have calculated barriers that are unreasonably high, in the range 35-50 kcal/mol. However, if proton transfer from solvent is combined with protic solvent stabilization of an ionic transition state, the calculated barriers are reduced to 5-15 kcal/mol, in good agreement with experiment. Thus the mechanism for amine or sulfide oxidation involves a protonated solvent molecule transferring a proton to the distal oxygen of the hydroperoxide in concert with a second molecule of solvent stabilizing the transfer of HO+ from the hydroperoxide to the nucleophile.