The internationalisation process of higher education space in Europe has resulted in joint-degree programmes and study programmes offered in foreign languages. This process is similar to globalisation trends in other spheres of social and economic life: intensified contacts and communication between people of different cultural backgrounds. Universities in Central Europe face a new reality which they were hardly ever prepared to deal with: teaching multicultural groups of students and using a foreign language as a medium of instruction and learning. The new situation calls for new requirements in the sphere of pedagogy, teaching methods and approaches and for a new range of competences of teachers involved in this process. Teachers must have some abilities, knowledge and skills to be able to master the cultural diversity and the intercultural communication process within their professional activities, such as teaching, guiding and coaching. This paper presents some aspects of the internationalisation of higher education in Slovakia and arguments for the need to raise teachers´ pedagogic and intercultural competences.