The oxidation reactions of ethylene, propene, dimethyl sulfide, trimethylamine, and trimethylphosphine with peroxynitrous acid have been studied computationally with the B3LYP, MP2, MP4, CISD, QCISD, and QCISD(T) levels of theory. The activation barriers for the alkene (ethylene and propene) epoxidations (18.4 and 15.5 kcal/mol at the QCISD(T)/6-31G*//QCISD/6-31G* level,respectively) and for the oxidations of dimethyl sulfide, trimethylamine, and trimethylphosphine (8.3, 4.6, and 0.5 kcal/mol at the QCISD(T)/6-31G*//B3LYP/6-31 1G** level, respectively) with peroxynitrous acid are similar to the barriers of their oxidations with peroxyformic acid and dimethyldioxirane, although these peroxides have very diverse O-O bond dissociation energies. Therefore, the feasibility of alkene epoxidation and the oxidations of methyl-substituted sulfides, amines, and phosphines by peroxynitrous acid should not differ significantly from those for peroxyformic acid and dimethyldioxirane. The transition structures for the epoxidation of ethylene and propene with peroxynitrous acid are symmetrical with equal or almost equal bond distances between the spiro oxygen and the carbons of the double bond. This symmetrical approach of the electrophilic oxygen is similar to that found for alkene epoxidations with peroxyformic acid. The geometries of the transition structures calculated at the QCISD and CISD levels are quite comparable to each other. The B3LYP calculated barriers for oxidations of alkenes, as well as sulfides, amines, and phosphines. are underestimated when compared with those calculated at the QCISD(T)//QCISD levels. The most economical and accurate protocol utilizes the B3LYP (for such "sigma-donors" as sulfides, amines, and phosphines) or CISD geometries with barriers calculated at the QCISD(T) level.