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The problem of achieving parallelism in the solution of the ordinary differential equations is investigated in this paper. The study focuses on an examination of block methods as a practical means for conveniently distributing the computational workload over multiple processors. Both previously suggested and newly proposed predictor-corrector formula pairs are presented and analyzed and a variable stepsize procedure is developed. The performance of two particular members of the block predictor-corrector class is evaluated experimentally using a collection of test problems. A multimicroprocessor system architecture which uses a distributed memory to deal with the interprocessor communications problem is described as a feasible hardware realization of the approach.