The Foundation Maison des Sciences de l’Homme (FMSH, Paris), created by Fernand Braudel, presents a project for co-funding of its international fellowship programmes for experienced researchers. In France, FMSH is one of the most important actors in postdoctoral international mobility for researchers in social sciences and humanities.Equipped with a large research library and hosting research programmes and centres mainly tied to CNRS, EHESS, Paris universities and the Fondation Nationale de Science Politique, FMSH is the largest establishment in the country for hosting and providing work facilities for researchers in social sciences and humanities from all over the world. At the postdoctoral level, FMSH has, for more than twenty years, managed international fellowship programmes for incoming researchers, along with an outgoing programme for researchers from French research institutions. These fellowship programmes are currently co-financed by CNRS, French ministries as well as by German and American private foundations. In the framework of these programmes, some 50 foreign postdoctoral fellows arrive each year to work in French research labs for 3 to 12 months, and 6 to 8 French fellows are sent for research in Germany, for 3 to 10 months. Annual volume is about 320 fellow-months. In addition, a large number of senior researchers are hosted (totalling more than 80 fellow-months), along with postdoctoral fellows with third-party financing (40 to 50 fellow-months). 33 countries are currently eligible for incoming fellowships, while only one is eligible for outgoing French fellows. The COFUND proposal's objectives are to: 1) broaden the list of eligible countries, especially for European countries; 2) increase the average stay from 6 to 9 months and create possibilities for foreign fellows to benefit from additional stays needed to complete their research project in institutes in France and other EU countries; 3) increase the number of fellows.