The authors study the diagnosability of discrete-event systems. Failure detection and isolation is an important task in the automatic control of large, complex systems. A discrete event system (DES) approach to the problem of failure diagnosis is proposed in this work. Two related notions of diagnosability of DES's in the framework of formal languages and a comparison of diagnosability with the related notions of observability and invertibility are introduced. A systematic procedure for detection and isolation of failure events using diagnosers is presented. A necessary and sufficient condition for a language to be diagnosable is given. The major advantage of the approach is that it does not require detailed, in-depth modeling of the system to be diagnosed. Comparisons are also made between the approach taken in this work and alternative approaches to failure diagnosis.