The aim of the paper is to identify and describe some specifics of intercultural competence development at the tertiary level in the framework of language and culture. Different views on intercultural competence development in higher education are presented as well as intercultural competence development in different countries and many scholars’ points of views. The results show certain specifics of intercultural competence development including linguistic competence, linguistic and cultural competence, as well as the components of intercultural competence development: the knowledge of foreign languages, cultural background knowledge, and basic soft skills. It is stated that knowing foreign languages, understanding the national culture of the target language, and having universal soft skills are necessary for successful intercultural competence development. Some soft skills are developed too, such as: tolerance, a sense of responsibility for one’s actions, the ability to empathy, understanding and acceptance of a foreign culture, the ability and desire to understand the difference and unity of one’s culture and the country culture of a target language, a sense of adequate and friendly perception of a foreign language and its realities. It is concluded that it is important to know a theory and have a practice for intercultural competence development and intercultural communication, since a foreign language, culture can only be acquired through activities. As for the specifics of intercultural competence development at the tertiary level in national universities, an indirect character of its development and patterning during intercultural communication are characterized.