Mixture cure models are usually used to model failure time data with long-term survivors. These models have been applied to grouped survival data. The models provide simultaneous estimates of the proportion of the patients cured from disease and the distribution of the survival times for uncured patients (latency distribution). However, a crucial issue with mixture cure models is the identifiability of the cure fraction and parameters of kernel distribution. Cure fraction estimates can be quite sensitive to the choice of latency distributions and length of follow-up time. In this paper, sensitivity of parameter estimates under semi-parametric model and several most commonly used parametric models, namely lognormal, loglogistic, Weibull and generalized Gamma distributions, is explored. The cure fraction estimates from the model with generalized Gamma distribution is found to be quite robust. A simulation study was carried out to examine the effect of follow-up time and latency distribution specification on cure fraction estimation. The cure models with generalized Gamma latency distribution are applied to the population-based survival data for several cancer sites from the Surveillance, Epidemiology and End Results (SEER) Program. Several cautions on the general use of cure model are advised. Copyright © 2004 John Wiley & Sons, Ltd.