Abstract This paper present the estimation of the stress-strength parameter R = Pr(X >Y), when X and Y are two independent exponential random variables with a different scale parameter but having the same location parameter based on hybrid censored samples. The maximum likelihood estimators (MLE) is obtained, the asymptotic distribution of the MLE of R is also obtained, and they have been used to construct the asymptotic confidence interval of R, the Bootstrap-t method is produced and Monte Carlo simulation is presented to evaluate the MLE estimation.   Key Words and Phrases: Hybrid censoring; two-parameter exponential distribution; maximum likelihood estimators; bootstrap confidence interval.