Independence is a concept of scholarly interest in relation to higher education, especially when it comes to undergraduate projects. At the same time independence is characterised by a certain conceptual ambiguity, and, consequently, tends to be understood differently in different academic contexts, both nationally, internationally and interdisciplinary. Based on the existing research in the field, we see a need for more studies on how supervisors of undergraduate projects handle this conceptual ambiguity. The aim of this article is, thus, to examine how supervisors from two different education programmes, teacher education and journalism, in two different countries, Sweden and Russia, understand the concept of independence within higher education in connection with the supervision of undergraduate projects. The analysis is based on 12 focus-group interviews with supervisors at different universities in the two countries. In our results, we highlight and discuss seven different understandings of independence that were recurrent in our material and in which phases of the undergraduate project they were seen as most significant. Using Wittgenstein's ideas on family resemblances, we conclude with a discussion of how the concept independence may be understood in relation to some associated concepts that are also significant within higher education.