In this paper two classes of multi-state systems are proposed and the concept of modules of those systems is clarified from mathematical aspects. The purpose of this paper is to investigate some properties of modules on basis of the minimal elements which determine the structure of systems. Furthermore, we discuss a criterion, what we call test for modularity", for deciding whether or not a subset of components is a module, and develop three modules theorem" which is well-known in the theory of binary-state coherent systems.