One of the major challenges to linguistic theory is the solution of what has been termed the "projection problem". Simply put, linguistics must account for the fact that starting from a data base that is both unsystematic and relatively small, a human child is capable of constructing a grammar that mirrors, for all intents and purposes, the adult system. In this article we shall address ourselves to the question of the learnability of a postulated subsystem of phonological structure: the stress system. We shall describe a computer program which is designed to acquire this subpart of linguistic structure. Our approach follows the "principles and parameters" model of Chomsky (1981a, b). This model is particularly interesting from both a computational point of view and with respect to the development of learning theories. We encode the relevant aspects of universal grammar (UG)--those aspects of linguistic structure that are presumed innate and thus present in every linguistic system. The learning process consists of fixing a number of parameters which have been shown to underlie stress systems and which should, in principle, lead the learner to the postulation of the system from which the primary linguistic data (i.e., the input to the learner) is drawn. We go on to explore certain formal and substantive properties of this learning system. Questions such as cross-parameter dependencies, determinism, subsets, and incremental versus all-at-once learning are raised and discussed in the article. The issues raised by this study provide another perspective on the formal structure of stress systems and the learnability of parameter systems in general.