The AFR Scheme, managed by the National Research Fund Luxembourg (FNR), supports postdoctoral research training projects in Luxembourg and abroad for up to 2 years. Researchers are eligible up to 8 years after their PhD. Particular importance is given to the selection of high-quality proposals, through a transparent and independent peer review. The scheme has a bottom-up approach, allowing researchers to freely choose their projects and host institutions, without thematic limitations. Nevertheless, for projects outside Luxembourg, beneficiaries must have a strong personal link and/or collaboration with Luxembourg.AFR grants greatly contribute to the improvement of working conditions and career perspectives of researchers: work contracts between AFR beneficiaries and their host institutions are considered as standard, with full social security including pension rights. Also, transnational mobility is mandatory. The scheme promotes public-private partnerships as a complementary path with growing importance compared to the classic academic career. Additional training and networking activities, organised by the FNR, further contribute to improving research careers in Luxembourg.In a country the size of Luxembourg (+/-500,000 inhabitants; +/-1,000 public-sector researchers), the AFR scheme has an important structuring effect.The AFR scheme funds two types of mobility:1) INCOMING: researchers from all nationalities doing a project in an eligible host institution in Luxembourg, and2) OUTGOING: researchers from any nationality carrying out their project in a research institution outside Luxembourg, but who have a link with the country, either through their origin or through a collaboration with a Luxembourg institution.Since 2 March 2009, the AFR scheme has received support under the COFUND action, for a total of 148 fellowship-years selected under calls in 2009 and 2010. The present COFUND proposal requests the extension of the funding for four years, for an additional 83 fellows (166 fellowship-years) to be selected in calls organised between December 2011 and end 2013. Beyond increasing the visibility of the scheme, extending the COFUND support allows to allocate a higher number of grants and to improve the working conditions of the fellows through the granted support measures.