The authors describe a method for fitting failure time mixture models that postulate the existence of both susceptibles and long-term survivors when covariate data are only partially observed. Their method is based on a joint model that combines a Weibull regression model for the susceptibles, a logistic regression model for the probability of being a susceptible, and a general location model for the distribution of the covariates. A Bayesian approach is taken, and Gibbs sampling is used to fit the model to the incomplete data. An application to clinical data on tonsil cancer and a small Monte Carlo study indicate potential large gains in e#ciency over standard complete-case analysis as well as reasonable performance in a variety of situations. R ESUM E Les auteurs decrivent une methode d'ajustement de modeles de melanges pour des temps de defaillance dans lesquels on postule l'existence de cas a risque et de survivants a long terme dans les situations ou les covariables ne sont pas ...