The first section of this paper deals with the properties any demand system should have if it is derived from any utility function. We find that the utility function under consideration could not be homogeneous if we impose the condition that the income elasticity is not one for all commodities. We then examine four mayor demand systems often used in empirical studies to see if they meet the properties listed in the first section. We find that Stone's linear expenditure system and Houthakker's indirect addilog system pass the theoretical tests, whereas the double log system and Theil's differential specifications do not. We fit the two theoretically satisfactory systems to Japanese data, and find that Stone's system explains the pattern of Japanese demand far better than Houthakker's. We, thus, suggest, on a theoretical as well as empirical ground, that Stone's linear expenditure system shall be the demand system in future econometric models in Japan.