This technical note introduces the notion of switched Discrete Event Systems (s-DES) and investigates its representational and computational potential in (i) the description and the analysis of the underlying DES behavior, (ii) the specification of the posed control requirements, and (iii) the eventual computation of the necessary control function. More specifically, it is shown that the potential decomposition of the overall DES behavior in a well defined set of "operational modes" enables the specification of control requirements and the synthesis of the corresponding control laws in a modular and distributed manner that takes full advantage of the aforementioned decomposition. The work is motivated by the need to cope with DES operating under a number of failing modes that result from non-catastrophic failures and repairs, and also DES that might evolve their operation through a number of "stages." Furthermore, the technical developments of the technical note and their representational and computational power are further highlighted by an application example that is drawn from the area of robot pursuit on time-varying graphs; however, due to space considerations, this example is provided in an electronic supplement to the technical note.