In this paper, we deal with the observability problem of a class of Hybrid Systems whose output is a timed string on a finite alphabet. We determine under which conditions it is always possible to immediately detect, using the observed output, when the system enters a given discrete state. We illustrate how to construct a Timed Automaton that is an abstraction of the given Hybrid System, and that preserves its observability properties. Moreover, we propose a verification algorithm with polynomial complexity for checking the observability of the Timed Automaton, and a constructive procedure for an observer of the discrete state.