In this article we have two primary objectives: (1) to elaborate in some detail a theory of phonological representations embedded within a parametric framework, and (2) to apply this theory to a particular vowel system which displays some rather interesting properties. This work is a continuation of a collaboration on a programme of research on phonological theory begun in 1982 (cf. Vergnaud 1982; Kaye & Vergnaud 1984; Kaye et al. 1984, 1985, in preparation).This programme incorporates the view that phonology is to be regarded as a system of universal principles defining the class of human phonological systems. These principles underdetermine given phonologies in certain specific areas. A complete phonological system consists, then, of these principles along with sets of parameter values. Taken together, the principles and language-specific parameter settings give a complete characterisation of the phonological system under study. In this model, a phonological system contains no rule component. The observed phonological phenomena result from a combination of the general principles governing phonological representations and structures and the parameter values in operation in the particular language. We view this line of research as a continuation of the development of a theory of markedness (cf. Chomsky & Halle 1968 (SPE); Kean 1975, 1979). At the moment of writing, this view of phonology remains a long-term objective of our research programme. However, an increasing number of phonological processes which were formerly considered to be manifestations of rules are now successfully derivable from the principles of Universal Phonology (UP) (cf. Kaye & Lowenstamm 1984, to appear).