This article addresses the growing demand for access to higher education and the conditions under which this is leading to a worldwide market. The supply of transnational (or cross-border) education and the export of educational services play an increasingly important role in fulfilling this demand. Pressures to further liberalize the global higher education market by extending the commitments under General Agreement on Trade in Services are analyzed in terms of implications and concerns. Furthermore, the European response to these global developments is considered, focusing on the question whether the Bologna Process is a sufficiently adequate response to the challenges of globalisation. Finally, some observations and comments are presented on the current discussion and the role and arguments of various actors in it.