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This paper presents a novel sequential learning algorithm for radial basis function (RBF) networks referred to as dynamic orthogonal structure adaptation (DOSA) algorithm. The algorithm enables the RBF network to on-line adjust its structure and weights to the identified dynamics with a compact network structure. It makes use of the well-known idea of error reduction ratio in orthogonal least squares (OLS) method for network pruning, and lakes advantage of a sliding data window for monitoring system dynamics. Simulation results of nonlinear dynamic system identification demonstrate the adaptive tracking ability and high learning speed of the proposed algorithm.