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This paper considers the parameter identification for a class of nonlinear stochastic systems with colored noise. We filter the input-output data by using an estimated noise transfer function and obtain two identification models, one containing the parameters of the noise model, and the other containing the parameters of the system model. A data filtering based recursive generalized extended least squares algorithm is proposed by using the data filtering technique, and a recursive generalized extended least squares algorithm is derived for comparison. Finally, an example is given to support the proposed algorithms. Compared with the recursive generalized extended least squares algorithm, the data filtering based recursive generalized extended least squares algorithm can not only reduce the computational burden, but also enhance the parameter estimation accuracy.