The Least Developed Countries (LDCs) category has been set up in 1971 to identify countries « caught in a trap » and to support them to move « out of the trap ». The category, if successful, aimed at the end to disappear. But after about half a century, the move out of the LDC category through the graduation process has only begun. It now takes place in the new context of the 2030 Agenda for Sustainable Development. The graduation of LDCs should then be considered as a step towards the Sustainable Development Goals (SDGs). This is the topic of the present brief.  Respective titles of two books , Guillaumont 2009, and the forthcoming companion volume Guillaumont, Edr, 2018.