In some clinical trials, one may see that a significant fraction of patients are cured and their original disease does not recur even after termination of treatment and pro-longed follow-up. This situation occurs frequently in pediatric cancer trials where there are excellent therapeutic results. In such cases, interest concentrated on the difference of cure rates rather than other types of differences in failure distributions. Various authors have investigated the parametric and nonparametric methods for testing the difference of cure rates. In this study, we compare by simulation the power and size of a parametric test and five nonparametric tests in a various range of the alternatives, censoring rates and cure rates. Our objectives are to determine if any test was preferable on the basis of size and power in various situation, and to investigate the effect of the model misspecification.