The need for neighbourness and Intercultural competences in Higher Education Institutions is ascending. This is because in recent times, there has been an increase in multicultural classrooms driven by globalization and the growth in global Internet connectivity. Globalization has enabled increased human mobility across physical national and cultural boundaries; while Internet connectivity has enabled virtual contact, interactions, and collaborations between persons from different cultures. Physical mobility, specifically for study abroad, results in physical multicultural classrooms. The purpose of this study is to provide an overview into the relevance of neighbourness in a multicultural classroom and challenges in a classroom that denotes the absence of neighbourness. The challenges are inspired and extracted from one-on-one Interviews with Higher Education Institution (HEI) teachers and foreign students from Finland, Italy, Denmark, Germany, Latvia and Turkey. Twenty people were interviewed. In the multicultural classrooms, six different challenges were identified as a result of analyzing the interview data. Those are language barriers, misunderstanding of cultural dispositions towards others, asymmetric communication, differences in cultural behavioral norms governing interactions, different styles of learning and problem with the familiarization with technology. [For the complete volume, "Proceedings of International Conference on Studies in Education and Social Sciences (Antalya, Turkey, November 11-14, 2021). Volume 1," see ED625228.]