AbstractAn adaptive blind source separation algorithm for the separation of convolutive mixtures of cyclostationary signals is proposed. The algorithm is derived by applying natural gradient iterative learning to a novel cost function which is defined according to the wide sense cyclostationarity of signals and can be deemed as a new member of the family of natural gradient algorithms for convolutive mixtures. A method based on estimating the cycle frequencies required for practical implementation of the proposed algorithm is presented. The efficiency of the algorithm is supported by simulations, which show that the proposed algorithm has improved performance for the separation of convolved cyclostationary signals in terms of convergence speed and waveform similarity measurement, as compared to the conventional natural gradient algorithm for convolutive mixtures. Copyright © 2004 John Wiley & Sons, Ltd.