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Multithreading has dominant paradigm in general purpose MIMD parallel computation. We consider the problem of scheduling multithreaded computations to achieve linear speedup without using significantly more space-per-processor than required for a single-processor execution. We begin by developing a formal graph-theoretic model of multithreaded computation and quantifiable measures of execution time and space. Based on these measures, we exhibit natural bounds to characterize efficiency with respect to time and space. Our first result shows that there exist multithreaded computations such that no execution schedule can simultaneously achieve an efficient time bound and an efficient space bound. By restricting ourselves to a class of computations we call strict, however, we show that for any number P of processors and any strict multithreaded computation, there exists an execution schedule that achieves both an efficient time bound and an efficient space bound. We give a centralized algorithm to compute such schedules, and we give a distributed algorithm that computes schedules with bounds that are nearly as good as the centralized algorithms. We also show that some nonstrictness can be allowed in an otherwise strict computation in a way that may improve performance, but does not adversely affect the time and space bounds.