This report investigates the process of focussing as a description and explanation of the comprehension of certain anaphoric expressions in English discourse. The investigation centers on the interpretation of definite anaphora, that is, on the personal pronouns, and noun phrases used with a definite article the, this or that. Focussing is formalized as a process in which a speaker centers attention on a particular aspect of the discourse. An algorithmic description specifies what the speaker can focus on and how the speaker may change the focus of the discourse as the discourse unfolds. The algorithm allows for a simple focussing mechanism to be constructed: and element in focus, an ordered collection of alternate foci, and a stack of old foci. The data structure for the element in focus is a representation which encodes a limted set of associations between it and other elements from teh discourse as well as from general knowledge.