Complex systems, which consist of different interdependent and interlocking subsystems, typically havemultiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as hybrid systems. This paper studies the conditions for dissipativity and some stability properties of a class of hybrid systems with multiple co-existing equilibrium points, modelled as nonlinear hybrid automata. A classification of equilibria for hybrid automata is proposed. The objective is to identify dissipative components as groups of discrete locations within the hybrid automaton, formed according to existing equilibria. An example is provided.