The goal of this thesis is to develop a parametric model of acquisition which incorporates the idea that phonological systems are underlyingly unspecified for certain feature values. I examine two variants of this model: one based on the theory of Radical Underspecification (Archangeli and Pulleyblank 1986), and one based on the theory of Contrastive Underspecification (Steriade 1987). I assume the principles and parameters framework, where the initial phonological system of the child is assumed to be characterized by the unmarked parameter settings of UG. The two types of parameters that are examined in detail are featural parameters and rule parameters. The unmarked settings of featural parameters are supplied by universal redundancy rules. In most cases, the unmarked settings of rule parameters are assumed to be OFF, or non-application. I provide analyses of the vocalic systems of Hungarian and Spanish, based on the parametric theories of Radical and Contrastive Underspecification, which demonstrate that certain phonological parameters in these languages must be reset to the marked option. The Hungarian analyses focus particularly on spreading processes, while those in Spanish focus on alternations that take place within verb conjugation classes. Given the differences between the initial child state and the adult phonological systems of Hungarian and Spanish, the underspecification acquisition models make certain predictions regarding acquisition in these languages. These predictions are then tested using data from children acquiring both Hungarian and Spanish. The early phonological systems of children acquiring Hungarian and Spanish are found to initially be smaller than predicted by either acquisition model. To account for these results, and still maintain a parametric model, I propose a theory of feature availability, which specifies the order in which features may become part of a child's phonological system. In conjuction with this theory of feature availability, the RU model is able to explain the development of children's early phonological inventories, as well as certain substitution patterns. The contrastive specifications required by the theory of CU cannot account for these aspects of the data. / Arts, Faculty of / Linguistics, Department of / Graduate