Almost all experimental investigations on concepts of time (T), distance (D) and velocity (V) since 1946 have been based on the Piagetian theory. However, there are several controversial points in Piaget's investigations. In the experiment described in this paper, developmental changes of concepts concerning relation of T, D, and V were examined using 148 children from 4- to 10-years-old and 20 undergardaute students, with the aim of addressing the controversy in Piaget's investigations. Results of these investigations include: (1) almost all children over 5 years of age could understand the proportional relation between D and T, and V and D through concrete operation, though they could not verbalize the reasons for their understanding; (2) it was difficult for young children to understand the inversely proportional relation between V and T even through concrete operations, but, the verbalization of reasons developed rather smoothly and rapidly after age 8; (3) in young children under 6-and-a-half-years-old, all relations between two variables seemed to be proportional and they seemed to pay little attention to the third constant variable; (4) over 8-years-old, most children correctly understood two proportional relations and one inversely proportional relation; and (5) it is not clear if children over 9 had the intercorrelational concept among three variables. (CW)