Trade globalisation is beginning to affect universities worldwide. In response to this outside pressure, institutions have become more geared to gaining international repute through research than to maintaining their reputation at home for the quality of their teaching. As a result of this focus on research, French universities, for example, are losing ground to other kinds of higher education institutions. One of the main reasons is that research encourages specialisation, whereas the market increasingly requires multi-disciplinary and cross-cutting skills. In order to explore how society's contradictory demands can be met, two opposing models will be presented, one that seeks to preserve the universalist role of universities and another that would prompt higher education institutions to become increasingly specialised in pursuit of research excellence. Between these two extremes, there is perhaps a middle way that is difficult to follow, but that is exceptionally enriching for the university community, provided that university management is rethought. The primary mistake that can be made in any process of change is to seek to merge the role of individuals with that of institutions. Although universities can continue to pull together all the various threads that contribute to economic development, individuals cannot be expected to have the same multi-faceted profile. This means that the quality of tomorrow's universities will depend on the quality of interpersonal relationships and how they are managed. (Contains 4 tables.)