The aim of the paper is to explore the presuppositions of intercultural dialogue on the background of the analysis and model typology of dialogical speech acts. One of the unexpected consequences of the postmodern developments in Western philosophy is a fundamental crisis of its traditional universalistic paradigm. A challenge to this paradigm is an ambitious pluralist one, which is rooted in cultural world diversity. The paper explores a justified philosophical response to a possible intercultural dialogue. It also asks the question what inherent elements and what types of dialogue should create the basis of such an "intercultural speaking".