Resumen: Controllability is studied for general classes of timed continuous Petri net (TCPN) systems, under infinite server semantics (ISS). For this, a new concept of controllability is introduced as an adaptation of the classical linear systems controllability one. For the case where all transitions are controllable, sufficient and necessary conditions for controllability, which are tested in polynomial time, are given. For the case with uncontrolled transitions, sufficient conditions for controllability, over a set of equilibrium points, and a necessary condition for reachability are introduced. In a forthcoming seminar we will speak about control laws for TCPN systems.