In this talk I will present the basic elements of a computational theory of discourse structure.^ A proper account of discourse structure is needed both as the basis of an account of discourse meaning (a semantic task) and to underlie a model of discourse processing. It provides the former by specifying the basic units a discourse comprises and the ways in which they can relate. It plays a key role in discourse processing by stipulating constraints on those portions of a discourse to which any given utterance in the discourse must be related.