The method of reverse osmosis was used to investigate the effects of inorganic and organic additives on the treatment of waters contaminated with cesium-137 and strontium-90. Sodium chloride was used as an inorganic additive while polyacrylamide was used as an organic additive. Treatment was carried out using an OFAM composite reverse osmosis membrane. It has been shown that the introduction of sodium chloride into the system treated results in worsening of the purification index (the retention factor for ions of cesium-137 and strontium-90) used by the membrane while the introduction of polyacrylamide improves the treatment of water contaminated with radionuclides. In addition, as polyacrylamide concentration increases the OFAM membrane coefficient of retaining radionuclides of cesium-137 and strontium-90 increases as well. The value of the transmembrane flux with the increase in the concentration of the polyelectrolyte decreases in the case of treatment of waters contaminated with strontium-90.