The invention relates to a process for the epoxidation of an olefin, wherein the concentration of the olefin oxide in the outlet is greater than about 2.2% by volume. More particularly, the invention relates to a process for the epoxidation of ethylene by contacting a feed including at least ethylene and oxygen with an improved epoxidation catalyst. The catalyst which has improved selectivity in the epoxidation process at high productivities, includes a solid support having a surface, which has a first mode of pores that have a diameter ranging from about 0.01 .mu.m to about 5 .mu.m and having a differential pore volume peak in the range from about 0.01 .mu.m to about 5 .mu.m. The surface also has a second mode of pores, which is different from the first mode of pores, having a diameter ranging from about 1 .mu.m to about 20 .mu.m and have a differential pore volume peak in the range from about 1 .mu.m to about 20 .mu.m. On the bimodal pore surface is a catalytically effective amount of silver or a silver-containing compound, a promoting amount of rhenium or a rhenium-containing compound, and a promoting amount of one or more alkali metals or alkali-metal-containing compounds.