Abstract
This paper deals with the explanation the maxim of relevance provides for the way utterances in argumentative discourse follow each other in an orderly and coherent fashion. Several senses are distinguished in which utterances can be considered relevant. It is argued that an utterance can be considered relevant as an interactional act, as an illocutionary act, as a propositional act, and as an elocutionary act. These four kinds of relevance manifest the rational organization of discourse, which is aimed at bringing about mutual alignment between the participants, enabling them jointly to work out certain interactional outcomes that are acceptable to both of them