From a double point of view, a longitudinal study was done to find out, whether a child's concept of space advanced through Piaget's stage: (1) Would a high degree order be found on the developmental course of a child's concept of space? ; and (2) would a mental homogeneity be found in it? For the study subjects were made of a 4-year-old and a 5-year-old group. They were required to perform seven kinds of tests on the concept of space, and conservation test. Results were as follows: (1) Means of each test, correlations between chronical age and each test showed that a child's concept of space advance in chronological order. But the transition from one stage to the next was vague, and many different features were found in the same stage.(2) The correlations among eight tests were found low. A common factor for all tests was not found, and the developmental course differedindividually. From these results, it was difficult to support Piaget's stage theory with homogeneity.