The article considers the institute of operation of a criminal statute in space and by personal scope of application through the prism of conflict regulation. Social relations, established due to the operation of the criminal statute in space and by personal scope of application, as well as the moment of collision between criminal law jurisdictions of different states are the object of the research. The subject matter of the research is: criminal codes of Russia and foreign states, international agreements of a jurisdictional nature. The author pays special attention to jurisdictional rules of the domestic law. In this paper the author uses the following research methods: dialectic, inductive, deductive, and other general scientific and specific scientific methods and ways of scientific knowledge. Special role is assigned to comparative law analysis. The author puts together a doctrine, based on the fundamental principles of the conflicts of laws for the purpose of creating a regulation system for criminal law jurisdictional conflicts. The article covers fundamental principles of the proposed doctrine, considers the structure of the conflicts of law rules and analyzes the current state of legislative regulation of criminal law jurisdiction. The author carries out a detailed comparative analysis of criminal laws in order to determine the most wide spread variants of regulation of criminal law jurisdiction, and proposes recommendations for legislative recognition of the territorial scope of validity of a criminal statute.