Epoxidation of ethylene, propylene, 2-methylpropene, trans-2-butene, 2-methyl-2-butene, and 2,3-dimethyl-2-butene were carried out in a flow-through reactor in the homogeneous gas phase at pressures of 0.25-1.0 bar in the temperature range of 250-375 degrees C. Residence times in the reactor varied from 8.3 to 38 ms. The oxidizing agent needed in the feed gas is ozone. The O-3 efficiency (reacted olefin/initial O-3) was found to be strongly dependent on the reactivity of the olefin used. For C-4-C-6 olefins, the O-3 efficiency was better than 75% in each case. For 2-methyl-2-butene and 2,3-dimethyl-2-butene, the O-3 efficiency exceeded the theoretical value of 100% considerably. The selectivity to epoxide was about 90% independent of the olefin used. Under conditions of nearly total olefin conversion, the high selectivity to the epoxide has been retained as unchanged. There were no indications for consecutive reactions of the epoxides.