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This paper deals with the problem of designing a distributed fault detection and isolation methodology for nonlinear uncertain large-scale discrete-time dynamical systems. As a divide et impera approach is used to overcome the scalability issues of a centralized implementation, the large scale system being monitored is modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a Local Fault Diagnoser is designed, based on the measured local state of the subsystem as well as the transmitted variables of neighboring states that define the subsystem interconnections. The local diagnostic decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the interconnection with neighboring subsystems. The use of a specially-designed consensus-based estimator is proposed in order to improve the detectability and isolability of faults affecting variables shared among overlapping subsystems. Theoretical results are provided to characterize the detection and isolation capabilities of the proposed distributed scheme. Finally, simulation results are reported showing the effectiveness of the proposed methodology.