The thesis represents a thorough review of linguistic theories of Valency and Case and their use in computational language processing in the fields of general Computational Linguistics, Artificial ...Intelligence and Machine Translation. The first part consists of a series of descriptions of approaches to Valency and Case: the Valency theories of Tesniere, and Helbig & Schenkel, among others, are especially singled out, and considerable attention is paid to the numerous proposals for distinguishing 'complements and 'adjuncts' found in the Valency literature. Subsequent chapters consider in detail Fillmore's various descriptions of his original views on Case, Anderson's 'locallst' Case grammar, the 'verb feature' approaches of Chafe, Cook, and Longacre, Starosta's 'Lexlcase' and Dik's 'Functional Grammar'. In the second part a broad view is taken of some specific problems for Case: the definition of the cases themselves, the problem of 'dual roles', and the 'one case per clause' constraint. Part III concerns the use of Case in Computational Linguistics, looking at a number of Case-based systems^ for various purposes including general parsing, speech recognition and question-answering systems. The Case-like approaches found in Bobrow & Winograd's KRL and in Minsky's 'frames' are considered, as is Schank's 'Conceptual Dependency' framework for knowledge representation. Machine Translation systems using Valency and Case are described, and a strategy for translation based on Valency and Case offered. In the final section, the author's own 'case grid' proposal for defining a case system is discussed.