In this article, internationalisation of higher education is analysed as a response to globalisation. A distinction is made between two paradigms in internationalisation: competition and cooperation. The different approaches to internationalisation in the Anglo-Saxon countries on the one hand and in continental Europe on the other are analysed along the lines of these two paradigms. With respect to the role and position of continental Europe in the global higher education market the following questions are explored. Is there a real higher education market in Europe and if so for whom? Should and can European higher education actually compete internationally, and if so, is cooperation the right strategy to do so? It will be concluded that the effectiveness of cooperation and especially that of international university consortia in international competition is largely still hidden in the future. Furthermore, many questions still remain to be answered in order to improve our understanding of the international higher education market in terms of its segmentation and the related diversification of the higher education sector and its functions.