The epoxidations of propene and isobutene with peroxyformic acid proceed by a concerted pathway via slightly unsymmetrical transition structures where the differences in the bond distances between the double-bond carbons and the spiro oxygen are only 0.021 and 0.044 Angstrom at the QCISD/6-31G* level. In contrast, the more polarizable nature of the carbon-carbon double bond of alpha,beta-unsaturated systems results in an unsymmetrical transition structure for the epoxidation of 1,3-butadiene with an order of magnitude difference in the carbon-oxygen bond distances of 0.305 Angstrom at the QCISD/6-31G* level. A highly unsymmetrical transition structure has been also found at this level for the epoxidation of acrylonitrile. Notwithstanding the difference in the extent of asymmetry of the transition structures, both epoxidations of methyl-substituted alkenes and such alpha,beta-unsaturated systems as 1,3-butadiene and acrylonitrile with peroxyformic acid follow a concerted asynchronous pathway. An unsymmetrical transition structure for 1,3-butadiene epoxidation and the concerted nature of the oxygen-transfer step are consistent with calculated kinetic isotope effects. The closeness of the barriers for propene and 1,3-butadiene epoxidations supports the conclusion that the reactions have similar mechanisms albeit they differ in the extent of asynchronous character of their transition structures. Methyl substitution leads to a decrease in the epoxidation barriers from 18.8 kcal/mol for ethylene to 13.7 kcal/mol for isobutene at the QCISD(T)/6-31G*//QCISD/6-31G* level. While the activation barrier for the epoxidation of I,3-butadiene with peroxyformic acid (15.9 and 11.7 kcal/mol at the QCISD(T)/6-31G* and B3LYP/6-31G* levels, respectively) is close to that for propane epoxidation (16.0 and 12.0 kcal/mol at the QCISD(T) and B3LYP levels, respectively), the barrier for acrylonitrile epoxidation is higher (21.0 kcal/mol at the QCISD(T)/6-31G* level). This increase in barrier height reflects the decreased nucleophilicity of double bonds bearing electron-withdrawing substituents. The energy differences between syn and anti configurations of the transition structures for the epoxidations of 1,3-butadiene and acrylonitrile with peroxyformic acid are very small (0.1-0.3 kcal/mol).