The article considers the disjunctive structures of argumentation from the point of view of their construction in the process of interaction drawing on the material of modern American political interviews. The analysis of examples, including the politician’s borrowing of the interviewer’s argumentation components, such as point of view and assumption, is conducted. As a result of consideration of the interactive characteristics of disjunctive argumentation, dependent argumentation, acting as a reaction to the politician’s reply, and independent argumentation, associated with the «interception» of the speech initiative are singled out. The specificity of these types of argumentation is determined. The analysis of argumentation is also carried out from the positions of the strategy of counter-argumentation and cooperative argumentation. The article describes the functioning of interactive elements of political interviews, in particular, discursive markers and ego-referential components. In addition, the disjunctive structure of argumentation is considered from the cognitive point of view, and a basic extensive model for the disjunctive argumentation is developed, implying the independence of its constituent arguments.