We propose to fit a recurrent feedback neural network structure to input-output data through prediction error minimization. The recurrent feedback neural network structure takes the form of a nonlinear state estimator, which can compactly represent a multivariable dynamic system with stochastic inputs. The inclusion of the feedback error term as an input to the model allows the user to update the model based on feedback measurements in real-time uses. The model can be useful in a variety of applications including software sensing, process monitoring, and predictive control. A dynamic learning algorithm for training the recurrent neural network has been developed. Through some examples, we evaluate the efficacy of the proposed method and the prediction improvement achieved by the inclusion of the feedback error term. (C) 2001 Elsevier Science Ltd. All rights reserved.