One of the international obligations which serves ground for the principle of the inevitability of punishment to realize is the international obligation “aut dedere aut judicare”. The historical origin of the international obligation takes its roots back to 2280 BC and to 19th century got its special accomplishment which is explicated in international treaties provisions. As the system of international corporation aimed at creating a flexible and sustainable mechanism for the international fight against certain types of crimes alternated, the legal nature and scope of the international obligation “to extradite or prosecute” has changed as well. The provisions of the international treaties provide for new alternative forms of the obligation to establish, e.g. “The Hague Formula”, the “Terrorism formula”, the “Drug formula”, the “Constitutional formula” and the formula for “Cooperation with authorities of the international criminal justice”. Each formula depends on the type of crime and assigns a priority for the execution of the exact part of the alternative obligation.