This article addresses the problem of communicative strategies for conveying criticism and disapproval in statements of appellative genre issued by presidents of American and British top universities. We claim that discursive representation of university chief leaders who are critically evaluating government decisions and incidents forms a linguistic and sociocultural communicative genre system with a set of effective rhetoric and communicative means. In academic administrative discourse, statements of appellative genre are characterized by dynamic application of positive and negative politeness strategies and regular reproduction of value-centered arguments, which update the system of values of the American and British academic communities. Discursive behavior of university chief academic administrators contains the rhetoric that appeals to logic, addressee’s emotions (pathos) and is based on the arguments to ethos, combining this with lexical and stylistic means that ‘threaten’ addressee’ face. Speakers use strategic tautology to increase the significance of the value system of an academic community. The concepts, themes, tasks, and tactical means, identified in the appellative statements of university leaders, contribute to the formation of the concept sphere of American and British academic communities. The results of this present study detail discursive and genre characteristics of the administrative academic discourse and the strategies of conflict (disapproving) discourse in particular. Communicative behavior of university leaders determined, on the one hand, by the value system and, on the other, by strategic aims of communication, can serve as a model of leadership communication and a resource for improving the competence of modern academic leaders.