This paper deals with the problem of predicting the number of components which fail in a future time interval in the case where the failure population is a mixture of two exponential distributions and sampling is censored at a predetermined test termination time. The joint predictive distribution of the number of failures from each sub-population and the corresponding marginal distributions are derived. Both the one-sample and the two-sample prediction problems have been considered. Sample sizes are taken as random variables having the Poisson distribution. Numerical examples are provided to illustrate the predictive procedures.