In this paper, we make use of an algorithm of Huffer & Lin (2001) in order to develop exact prediction intervals for failure times from one-parameter and two- parameter exponential distributions based on doubly Type-II censored samples. We show that this method yields the same results as those of Lawless (1971, 1977) and Like w (1974) in the case when the available sample is Type-II right censored. We present a computational algorithm for the determination of the exact percentage points of the pivotal quantities used in the construction of these prediction intervals. We also present some tables of these percentage points for the prediction of the ’ th order statistic in a sample of size n for both one- and two-parameter exponential distributions, assuming that the available sample is doubly Type-II censored. Finally, we present two examples to illustrate the methods of inference developed here.