Mixture models incorporating the long term survival of some individuals are encountered in many important fields of applied science. In particular, these models arise in biomedical and criminological studies. This paper is concerned with the consistency and asymptotic normality of the maximum likelihood estimates for the parameters underlying the mixed-exponential model with long-term survivors for randomly censored data. It is shown that these properties can only be anticipated if the data are not too heavily censored, relative to the underlying failure rate and the proportion of the long-term survivors.