We consider five notions of decompositions of Semi-Thue-Systems. These are interesting in view of the theory of Semi-Thue-Systems as well as in regard to practical applications (simplification of the analysisproblem). The decompositions form a simple hierarchy. We proof a necessary and sufficient condition for each of the decompositions. Three of the notions are shown to be determinable in general, the other two notions are determinable only for contextfree Semi-Thue-Systems. © 1969 Springer-Verlag.