We present a new application of the abstract interpretation by means of convex polyhedra, to a class of hybrid systems, i.e., systems involving both discrete and continuous variables. The result is an efficient automatic tool for approximate, but conservative, verification of reachability properties of these systems. 1 Introduction Timed automata [AD90] have been recently introduced to model real-time systems. A timed automaton is a finite automaton associated with a finite set of clocks, each clock counting the continuous elapsing of time. Each transition of the automaton can be guarded by a simple linear condition on the clock values, and can result in resetting some clocks to zero. A nice feature of this model is that it can be abstracted into a finite state system, and that all the standard verification problems (reachability, TCTL model-checking [ACD90, HNSY92]) are decidable. However, many interesting extensions of this model have been shown to lose this decidability propert..