SUMMARYIn this paper, a modified least-squares method is proposed to treat the problem of identifying closed-loop systems in the presence of coloured noises. Using the information obtained by the standard least-squares (LS) method, some linear equality constraints of the estimated parameters are derived for extracting the estimation bias from the LS estimates. With the bias removed, consistent parameter estimates are obtained. It is shown that the presented method can achieve consistent parameter estimation without the modelling of the noises. The theoretical analysis is verified by numerical examples.1998 John Wiley & Sons, Ltd.