This paper discusses the structural identifiability of compartmental systems. This concept is related to the following problem: Given an input-output observation, and given a priori knowledge of graphical structure of interconnections of compartments, can we uniquely determine the unknown rate constants? This is an important and fundamental problem for determining the structure of compartmental systems. We pose a new definition of structural identifiability (abbreviated to SI) to avoid the confusion and misunderstanding appearing in the literature, and then give an algebraic equivalent condition for SI. Based upon this result, we obtain a new aspect to the SI: Concerning driving point systems, if a compartmental system is SI, the dual system whose paths are in reverse directions is also SI. If an open system is SI, the closed system is SI and vice versa. Concerning transfer systems, if a closed system is SI, then the open system is SI.These results would be useful to obtain the complete answer for the structural identifiability of compartmental systems.