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One of the important potentials of multiprocessor systems is the ability to speed the completion of a computation by concurrently processing independent portions of the job. In this paper we consider the static scheduling of computations for a system containing two indentical processors. The object is to complete the computation in the minimum amount of time. A computation is assumed to be specified as a partially ordered set of tasks and the execution time for each task. A solution for the two-machine case with preemptive scheduling is presented.