A new method for preparing supported silver catalysts with a narrow particle size distribution has been developed. For crystals with a diameter ranging from 100 to 1000 Angstrom the dependencies of reaction rates on size have been studied for epoxidation and deep oxidation of ethylene. For particles 300-500 Angstrom in size the reaction rate was found to increase sharply. The concentration of ethylene pi-complexes with Ag+ cations increased proportionally to the reaction rate. These pi-complexes are assumed to be the only intermediates directing the reaction towards epoxidation. The ratio of the reaction rate to the concentration of pi-complexes was found to remain constant within a wide range of AE crystal sizes including bulk silver samples. The influence of the support (alpha-Al2O3, SiO2) on the size effect relates to the secondary processes of ethylene oxide conversion. The factors that cause the catalytic size effect and the promoting effect of Cs are discussed.