This paper discusses diagnosis problems in distributed systems within the context of a language- theoretic discrete event formalism. A distributed system is seen as a system with multiple spatially separated sites with each site having a diagnoser that observes some of the events generated by the system and diagnoses the faults associated with the site. We allow the diagnosers to share information by sending messages to each other. Distributed systems are classified as being centrally, decentrally, and independently diagnosable. We characterize the class of distributed systems for which there exists a centralized diagnoser but there exists no inter-diagnoser messaging scheme that can replicate the information available to a centralized diagnoser. Plant properties that are necessary and sufficient for the three kinds of diagnosability are derived. The formulation and results are motivated by a discussion on the diagnosis of failures in a wireless LAN used to support the real-time operation of automated vehicles.