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This paper compares the performances of a multilayer perceptron neural network (MLPN) and a radial basis function neural network (RBFN) for online identification of the nonlinear dynamics of a synchronous generator in a power system. The computational requirement to process the data during the online training, local convergence, and online global convergence properties are investigated by time-domain simulations. The performances of the identifiers as a global model, which are trained at different stable operating conditions, are compared using the actual signals as well as the deviation signals for the inputs of the identifiers. Such an online-trained identifier with fixed optimal weights after the global convergence test is needed to provide information about the plant to a neurocontroller. The use of the fixed weights is to provide against a sensor failure in which case the training of the identifiers would be automatically stopped, and their weights frozen, but the control action, which uses the identifier, would be able to continue.