The ‘duty to extradite or prosecute’ refers to the requirement placed on theState where an accused of international crimes was arrested either toprosecute the accused in its own domestic courts or to extradite him or her tothe State which has requested their extradition. There is no doubt about thetreaty-based nature of this obligation, but there exist huge controversies onwhether such an obligation is customary or not. Some consider it merely as atreaty rule while, in contrast, some others deem it not only to be a customaryrule but a jus cogens obligation on the grounds of international crime. Ofcourse, there are paradoxical measures in States practice regarding theapplication of this duty. Nevertheless, the increasing number of treaties thatcontain such an obligation, acceptance of this obligation by various States,and the broadening of state measures to perform it, are all indicative ofpreparing the ground for this obligation to become a customary rule.Moreover, this obligation was set forth before the International Court ofJustice in the Lockerbie Case in 1992 and Belgium against Senegal Case(aut dedere aut judicare) in 2009. The World Court’s judgment in 20 July2012 will play a major role in the development of this rule in InternationalCriminal Law.Keywords:Custom, Extradition, Prosecution, International crimes, International Courtof Justice, Crimes against humanity, War crimes, International obligation,Criminal jurisdiction, Criminal punishment, Convention against Torture