In this paper, the actuators and sensors fault detection and localization using a system model is considered. To obtain the system model, the neural network modeling is used. The artificial feedforward neural network with dynamic neurons in the state-space representation is proposed. To estimate the neural network parameters, the Adaptive Random Search algorithm with projection is used. To identify, which of actuators or sensors is faulty, the system input estimator is proposed. The input and output residuals being the difference between the system input and output and its estimates are used to detect and isolate the faults. The final part of the paper presents an application study, which clearly confirms the effectiveness of the proposed approach.