A weighted least squares (WL-S) based adaptive tracker is designed for a cl ass of Hammerstein systems. It is p roved that the tracking error is asymptotically minimized. Incorporating with the diminishing excitation technique, the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved. Numerical examples are given and the simulation results are consistent with the theoretical analysis. (C) 2009 Elsevier Ltd. All rights reserved.