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The problem of fault detection and isolation/identification (FDI) of nonlinear systems using neural networks is considered in this paper. The proposed FDI approach employs recurrent neural network-based observers for simultaneously detecting, isolating and identifying the severity of actuator faults in presence of disturbances and uncertainties in the model and sensory measurements. The neural network weights are updated based on a modified dynamic backpropagation scheme. The proposed FDI scheme does not rely on the availability of full state measurements. In most works in the literature the fault function acts as an additive term on the actuator, whereas in this work the fault acts as a multiplicative term. This will make the formal stability and convergence analysis of the overall FDI scheme nontrivial and challenging. Our stability analysis considers the presence of plant and sensor uncertainties through the use of Lyapunov's direct method with no restrictive assumptions on the system and/or the FDI algorithm. The performance of our proposed FDI approach is evaluated through simulations that are performed for two case studies, namely FDI of 1) reaction wheel type actuators that are commonly utilized in the attitude control subsystem (ACS) of a satellite and 2) actuators in a two-link flexible joint manipulator.