Closed-form expressions for the first two moments and the product (linear) moments of the double exponential order statistics are obtained. Expressions for generalized least squares estimates of location and scale parameters based on symmetrically censored samples and for their variances are also obtained. Expected values of order statistics in random samples of sizeNdrawn from the standard double exponential population are evaluated accurate to six decimal places forN= 2(1)20 and these are presented in Table 1. The covariances of these order statistics, accurate to five decimal places are given in Table 2 forN= 2(1)20. Least squares estimates of location and scale parameters of the double exponential population, using ordered observations in complete and all possible symmetrically censored samples are presented in Table 3, accurate to four decimal places, forN= 2(1)20.