Recent developments by Hewitt and others have stimulated interest in message-passing constructs as an alternative to the more conventional applicative semantics on which most current languages are based. The present work illuminates the distinction between applicative and message-passing semantics by means of the &mgr;-calculus, a syntactic model of message-passing systems similar in mechanism to the &lgr;-calculus. Algorithms for the translation of expressions from the &lgr;- to the &mgr;-calculus are presented, and differences between the two approaches are discussed. Message-passing semantics seem particularly applicable to the study of multiprocessing. The &mgr;-calculus, through the mechanism of conduits, provides a simple model for a limited but interesting class of parallel computations. Multiprocessing capabilities of the &mgr;-calculus are illustrated, and multiple-processor implementations are discussed briefly.