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In this article, the joint best linear unbiased predictors (BLUPs) of twofuture unobserved order statistics, based on a set of observed orderstatistics, are developed explicitly. It is shown that these predictors aretrace-efficient as well as determinant-efficient BLUPs. More generally, theBLUPs are shown to possess complete mean squared predictive error matrixdominance in the class of all linear unbiased predictors of two futureunobserved order statistics. Finally, these results are extended to the case ofsimultaneous BLUPs of any $l$ future order statistics.

On simultaneous best linear unbiased prediction of future order statistics and associated properties