Intercultural group work (IGW), where students from different nationalities work together, is one important way to develop intercultural competence, a key skill for engineering students. This longitudinal, qualitative study of five master's engineering students follows their individual experiences in IGW and the affordances and challenges this way of working provides. In particular, the study problematises the use of the terms 'home' and 'international', often used to differentiate student experiences in IGW, by highlighting the range of student backgrounds and experiences which can be encompassed within them. The results show that the students' self-positioning in their group and their sense of belonging to it are affected by a range of factors including previous experience, the nature of the group work and personal aspects such as openness and adaptability. In addition, belonging to the group can be a transient process influenced in part by critical incidents during the group work process.