Mediation is an alternative dispute resolution process that is becoming more and more popular particularly in English-speaking countries. In contrast to traditional litigation it has not benefited from technological advances and little research has been carried out to make this increasingly widespread practice more efficient. The study of argumentation in dispute mediation hitherto has largely been concerned with theoretical insights. The development of argumentation theories linked to computational applications opens promising new horizons since computational tools could support mediators, making sessions (...) quicker and more efficient. For this, we need tools for close analysis of mediation discourse in order to explore the argumentative activity in depth, and ultimately get an accurate image of how dialogues unfold in this particular context. This paper therefore aims at laying the foundations of a theory of close analysis for discourse in dispute mediation. Theories provided by the literature serve as a basis for argumentative analyses of transcripts of mediation sessions in order to deliver a clear image of the argumentative structure. Analyses of the argumentative strategies in mediation discourse will allow for the development of a dialogue protocol that can be used to develop operational models which can be embodied in software to help make the mediation process easier and more effective. (shrink)