The paper considers the necessity of developing the intercultural communicative competence of university students. Russian authors who made a significant contribution to the study of intercultural communicative competence are considered. The article proves the importance of interdisciplinary approach for creating a methodology of developing the intercultural communicative competence of undergraduate students in the process of teaching two disciplines: introduction to intercultural communication and the foreign language. The terms of exercise, system, subsystem, complex, series, cycle, group of exercises in the methodology of teaching foreign languages are considered. A number of exercises for the implementation of the author's methodology is proposed. It includes four types of exercises: preparatory exercises; text-centric exercises; exercises organizing virtual intercultural communication; reflexive result exercises. The tasks of the exercises are listed. The concept of «film text» is presented, which is a special type of text performing a communicative function and has universal textual categories. The examples of exercises of different types are given. The exercises have heuristic, interactive, emotionally-semantic, multipurpose characteristics. The algorithm for working with the text in the format of debate is described in detail. The principles on which intercultural communicative competence of undergraduate students is based are analyzed.