This paper presents the results of a study done for a chapter in Managing academic support services in universities, edited by T. Hanson and published by Facet in 2005. Convergence means the merger or structural co-operation between library services, computing (or ICT) services, educational development services or other academic support services, particularly in higher education. In Britain and the U.S. convergence is now well established and the book includes a number of case studies. This study aimed to establish the state of the art of convergence in Europe outside Britain. The conclusion, as expected, was that convergence is rare or non-existent in continental European countries, except in Germany and Finland, where there have been significant initiatives. The paper will explore the reasons for this and whether the situation will change in the future.