This paper addresses the problem of determining the diagnosability of hybrid systems by abstracting hybrid models to a discrete event setting. From the continuous model the abstraction only remembers two pieces of information: indiscernability between modes (when they are guaranteed to generate different observations) and ephemerality (when the system cannot stay forever in a given set of modes). Then, we use standard discrete event system diagnosability algorithms. The second contribution is an iterative approach to diagnosability that starts from the most abstract discrete event model of the hybrid system. If it is diagnosable, that means that the hybrid system is diagnosable. If it is not, the counterexample generated by the diagnosability procedure is analysed to refine the DES. If no refinement is found, then it can not be proved that the hybrid system is diagnosable. Otherwise, the refinement is included in the abstract DES model and the diagnosability procedure continues.