The study examines how participants in mediation sessions treat fallacies in naturally-occurring argumentative discussions and with what consequences for their development. Taking an interactional approach to studying fallacies, the research sheds light on the nature of fallacies, how they are achieved, and what they are accomplishing in the course of interaction. The fallacies are considered to be breaches of the interaction order and/or the institutional order. Two types of fallacies that occur in the process of these interactions are distinguished: traditional (i.e., fallacies that date back to Aristotle's time and are widely recognized by argumentation researchers) and non-traditional (i.e., wrong moves that do not belong to the traditional list of fallacies but, nevertheless, were treated as such by recipients themselves in the process of interaction). The findings show that whether an argumentation move is considered to be fallacious or non-fallacious depends on the orientation of participants themselves to this interaction phenomenon and on the context it is used in. The research provides the support for the idea that the participants' responses are crucial for realizing the potential of the fallacious moves.