This article is about the text of the Draft Articles on Crimes Against Humanity temporarily adopted by the International Law Commission at its sixty-eighth session in 2016. It cannot be ruled out that the adopted text could subsequently be amended to take into account the evolution of the discussions within the International Law Commission. The final version of the Draft Articles ishighly anticipated by internationalists, all the more since in 2014, the Commission already observed in what constituted a “Final Report” on the theme of the obligation to extradite or prosecute (aut dedere aut judicare) that the existing treaty regime contained significant limitations as concerns the obligation to extradite or prosecute, which might need to be addressed. Amongst others, the Commission noted the absence of international treaties containing this obligation as relates to crimes against humanity. Also, the Commission reminded that it had placed this issue on its work programme, in the context of which was considered the elaboration of a new instrument on the prevention and repression of crimes against humanity that would include an obligation to extradite or prosecute the authors of these crimes. As adopted to this day, the text clearly provides, on the one hand, that crimes against humanity, should they be committed in times of armed conflict or not, are crimes under international law that states have committed to prevent and punish. On the other hand, it provides that states must cooperate in this respect, including through the obligation to prosecute or to extradite or to surrender. However, as appears from this analysis, there exists no obligation for states to try the presumed authors, nor to punish them. The obligation actually consists of the state submitting the case to its competent authorities for the exercise of criminal action. This does not mean, neither, that there exists an obligation to bring criminal charges, inasmuch as these authorities retain control on the initiation of proceedings. They are also free to not pursue the case without this decision resulting in a breach of the obligation imposed on the state under which they are acting, to prosecute the suspect without extraditing him or her, or to surrender him or her to a competent international jurisdiction.