This paper is centred on family conversations and focuses on the conditions that allow a specific strategic maneuver, the invocation of the authority, to be an effective argumentative strategy when used by parents to convince their children to accept rules and prescriptions. Within a corpus of argumentative sequences selected from 30 video-recordings of family mealtime conversations, an argumentative sequence between parents and children, which brings to light the results obtained through the qualitative analysis of a corpus of 60 argumentative sequences, is presented and discussed. The analysis relies on a communicative-argumentative methodology based on the extended pragma-dialectical theory and on the Argumentum Model of Topics to identify the participants' moves and to analyze the inferential configuration of arguments, respectively. The findings of the analysis show that the invocation of the authority by parents represents an argumentative strategy that is effective when two conditions are met: (i) the nature of the relationship between the person who represents the authority and the person to whom the argument is addressed is based on the certainty of positive feelings, rather than on the fear of punishment, and (ii) the reasons the prohibition is based on are not to be hidden from the child's eyes, but are to be shared by family members. The analysis has thus brought out a specific type of invocation of authority that we have defined as the authority of feelings. The results of this study contribute to research on family argumentation and on the interactional dynamics between parents and children. Copyright © 2012 John Wiley & Sons, Ltd.