The well known Shewharts control chart for mean is constructed under the assumption that the distribution of underlying quality characteristic is normal. It is known that the performance of this control chart is seriously degraded if the underlying distribution is different from normal. Since in many real life situations the distribution of the quality characteristic is not known several authors have suggested use of nonparametric control charts. In this paper we use simulation to study the performance of three of these nonparametric control charts: the median chart (Janacek and Meikle, 1997), the boostrap control chart (Liu and Tang, 1996) and Hodges-Lehmann control chart (Alloway and Raghavachari, 1991) for different distributions of the quality characteristic. The in-control and out-of-control run length properties of these charts are compared against that of the control chart for mean with estimated control limits. The run length properties of all these control charts are found to be dependent on the reference sample drawn. The Hodges-Lehmann control chart is seen to perform best among all the charts considered in this study. Note: For softcopy of this paper, please contact the authors - email: arnab@iima.ac.in