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This paper proposes a specification-based monitoring approach for automatic run-time detection of software errors and failures of distributed systems. The specification is assumed to be expressed in communicating finite state machines based formalism. The monitor observes the external I/O and partial state information of the target distributed system and uses them to interpret the specification. The approach is compositional as it achieves global monitoring by combining the component-level monitoring. The core of the paper describes the architecture and operations of the monitor The monitor includes several independent mechanisms, each tailored to detecting specific kinds of errors or failures. Their operations are described in detail using illustrative examples. Techniques for dealing with nondeterminism and concurrency issues in monitoring a distributed system are also discussed with respect to the considered model and specification. A case study describing the application of the prototype monitor to an embedded system is presented.