Abstract: The authors of the article present a comprehensive study of doctrinal approaches concerning the problem of the correlation of international and domestic law, based on multilevel, non-linearity of legal norms. The object of the article is the traditional doctrines of dualism (pluralism) and monism, an assessment of the circumstances of their emergence, the essence of approaches and subsequent transformation under the influence of globalization and integration processes. The authors analyze the theoretical foundations of the methods and conditions for integrating the norms of international law into the national legal system and the role of international law for the modern legal order. The authors were based on the methods of theoretical synthesis, induction and generalization, the principle of historicism. Among the special-legal - method of comparative jurisprudence, the main conclusions of the study are the assessment of traditional doctrines from the modern perspective of globalization and the integration existing in the modern international community. The practical situation continues to provide the ground not so much for the "improvement" of the doctrine, but for its revision and modern assessment, which makes it possible to designate the role of the international legal order for national jurisdictions.