A hybrid system is a system containing both of time-evolving
components and event-driven components. A formal approach is explored
in this paper, based on Extended Duration Calculus (EDC), for the
development of hybrid systems. A typical example of hybrid system from
modern control theory, a two-level adaptive control system is used for
illustrating our approach. Its high level consists of an event-driven
supervisor which reacts to the change of plant structure, and its
time-evolving low level consists of adaptive controllers and other
components.  Firstly performance specifications and system
specification of the case are formulated in EDC; then they are refined
stepwisely into specifications of the supervisor and the low level
components. Our approach emphasizes the interface between the two
kinds of components in the hybrid system.