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In this study, neuro‐fuzzy‐based identification procedure for Hammerstein model with coloured noise is presented. Separable signal is used to realise the decoupling of the identification of dynamic linear part from that of static non‐linear part, and then correlation analysis method is adopted to identify the parameters of the linear part. Furthermore, by combining multi‐innovation and gradient search theory, multi‐innovation‐based extended stochastic gradient approach is derived for improving the parameters estimation accuracy of the non‐linear part and the noise model. In addition, the convergence analysis in the martingale theory illustrates that the parameter estimation error will converge to zero under the persistent excitation condition. Finally, two simulation results demonstrate that the proposed approach has high identification accuracy and good robustness to the disturbance of coloured noise. [ABSTRACT FROM AUTHOR]