There is provided a process wherein a lower alkyl ester of a fatty acid derived from natural fats and oils and a lower alcohol containing 1 to 4 carbon atoms is produced in a lower sulfur content at lower costs without causing a reduction in yield and a deterioration in selectivity, as well as a process for producing an alcohol without reducing the activity of a catalyst. The process comprises the step of adsorption treatment of an ester with at least one adsorbent selected from clay and activated carbon. Further are provided a process for producing an ester which further comprises adsorption treatment with a hydrogenating decomposition-type adsorbent containing Ni and/or Cu, in hydrogen or a mixed gas atmosphere of hydrogen and an inert gas, and a process for producing an alcohol which comprises hydrogenation reaction with an ester produced by any one of these processes as the starting material.