The discrete event theory of supervisory and state feedback control offers many advatages for implementing supervisory systems. Algorithmic concepts have been introduced to ensure that the supervising algorithms are correct and meet the specifications. In the current methodology, it is, in general, assumed that the supervisory specifications are invariant during the operation of the system or, at least, until a given supervisory task is completed. However, there are many practical applications where the supervising specifications need to be updated in real time. For example, when dealing with complex processes, the tasks of supervisory systems analysis and synthesis can be facilitated by partitioning the controlled Discrete-Event System (DES) into several subprocesses. This partitioning is based on operational or physical considerations and a unique supervisor is assigned to control each subprocess at a given instant of time. When a decision maker at a higher level of hierarchy decides to change the supervising algorithm, switching to a new supervisor takes place. For this adaptive implementation, the decision-maker or coordinator first decides the set of acting supervisors based on the requested supervisory tasks or current system performance requirements and then exercises control over the enabled supervisors in real time. Specifically, in a Reconfigurable Discrete Event System (RDES) architecture, a bank of supervisors is defined to accommodate each identified operational condition or different supervisory specifications. This adaptive supervisory control system can change its supervisory configuration to accept coordinator commands or to adjust for changes in the controlled process. This paper addresses reconfiguration at the supervisory level of hybrid systems along with the underlying architecture of RDES. In particular, the paper reviews the supervisory control theory in the state-based framework and extends it to the paradigm of RDES, considering process control applications. The paper addresses theoretical issues with a limited number of practical examples. This control approach is particularly suitable for hierarchical hybrid implementations with the capability of reconfiguration at both the control and supervisory levels.