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The main aim of this paper is to synthesize a distributed adaptive sliding mode observer scheme for fault diagnosis of large-scale nonlinear dynamical networks. Each node dynamics includes both linear and nonlinear terms and the nodes are interconnected by a time-varying coupling strength. The key advantages of the developed adaptive observer are that its synthesis relies only on the dynamics of an individual node, its adaptive feature allows it to cope with bounded uncertainties and faults without a priori knowledge of their bounds and finally only local information exchange among the interconnected nodes are required. Moreover, faults severity in each node can be estimated from the principle of equivalent control. The efficiency of the proposed design approach is demonstrated using simulation studies for a network of coupled Chua oscillators.