In this paper we propose a hybrid system modeling framework aimed at analyzing diagnosability. In this framework, the hybrid system is seen as the composition of an underlying discrete event and an underlying continuous systems. Diagnosability of these two underlying systems are fully analyzed and new results are provided for the underlying continuous system (called the multimode system). Based on these results, a hybrid language that contains ‘natural’ discrete events and discrete events capturing the continuous dynamics, is defined. On the basis of this language the diagnosability definition of hybrid systems is provided. With respect to this definition, we prove that the diagnosability of the underlying continuous or the discrete event system is only a sufficient condition. Diagnosability of hybrid systems must be decided by coupling both discrete event and continuous informations. Finally, the necessary and sufficient condition of hybrid diagnosability is given.