The article, based on the study of doctrinal developments and the practice of states, reveals the issue of national legislation as a source of the obligation to extradite or prosecute (aut dedere aut judicare). The article highlights the position of the UN International Law Commission on the role of national legislation and state practice in implementing the obligation to extradite or prosecute; the practice of certain states (Finland, Estonia, Macedonia, Azerbaijan, Ukraine) regarding the legal establishment of the obligation to extradite or prosecute is considered; the measures that states should follow at the national level in order to effectively implement the principle of aut dedere aut judicare are defined.
 The article establishes that the determination of the legal nature and scope of the obligation aut dedere aut judicare is possible through the study of various types of sources in which this obligation is established (treaties, customs, international and national court decisions, national legislation of states). The obligation to extradite or prosecute has traditionally been established by international treaties of various types, the number of which is constantly increasing. The participation of many states in such international treaties (of a universal, regional or bilateral nature) is a reflection of the existing national practice of the states regarding the implementation of the principle of aut dedere aut judicare.
 It is substantiated that, along with treaties and customary (at least for the most serious international crimes) enshrining the principle of aut dedere aut judicare, national criminal law is an important source of the obligation to extradite or prosecute. The effective implementation of the principle of aut dedere aut judicare in each specific case will depend on the state’s fulfillment of both its international obligations and the implementation of the necessary measures (in particular, regarding the establishment of jurisdiction over offenders and criminal offenses) defined in national legislation with regard to extradition and prosecution.
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