The process of ethylene epoxidation under the effect of gas phase thermal oxidation of methane has been studied. It was shown that if methane oxidation is carried out in the first section of two-sectional reactor and ethylene is injected into the second section then epoxidation occurs as a result of interaction of ethylene and peroxy radicals generated by methane oxidation reaction. The dependence of ethylene oxide accumulation rate on methane/oxygen ratio in the first section of reactor as well as flow velocity and temperatures in the first and second sections has been studied. The results show that in the second section of the reactor the ethylene epoxidation takes place trough C2H4 + RO (2) (center dot) -> C2H4O + RO reaction.