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In order to be able to take full advantage of a distributed computing facility it is important not only to distribute the hardware but also to distribute the control of these resources. However, distributed control is very different from centralized control since at any time, several processes or several controllers may observe different and inconsistent views of the global system state. The task of scheduling jobs in a distributed system must also be done Without full knowledge of the system state. In this correspondence we define a totally new distributed scheduling algorithm LP (linear predictive). scheduling, which not only implements distributed control of task scheduling but is also able to adapt itself to workload fluctuations. Using a general-purpose distributed system simulator we have shown the performance rnitince advantages of this new algorithm.