In this paper the authors introduce several notions of stability for event graph models, timed or not. The stability is similar to the boundedness notion for Petri nets. The event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions. The controller itself is composed of an event graph. In this framework the authors solve the corresponding stabilization problems, i.e., they wonder if such a controller may prevent the explosion of the number of tokens.