The article is devoted to the analysis of the essence of international law, the nature of its sources and the role of courts in the formation of its norms. This process is demonstrated by the example of the practice of the Court of the Eurasian Economic Community and the Court of the Eurasian Economic Union as a judicial body of an integration org anization. The author summarizes the work of the Court over the first 12 years of its functioning, lists achievements and unresolved issues. The author concludes that the main source of international law is custom – repeated rules of behavior in similar situations, recognized as mandatory. In repeated judicial positions, a uniform judicial practice is formed – judicial custom, which serves as an instrument for the formation of international law: the court creates a legal position, which over time may become a rule of law. In th e practice of the Court of the EAEU, generally recognized (general) principles of law turned out to be the most relevant source of law. The j udgments and advisory opinions deliv ered by the Court of the EAEU have a direct impact on the economy and social relations of all member states of the Union in areas within the competence of the integration organization. Currently, the most important aspects of the Court’s activities that require reform are the procedure for selecting and appointing judges, the rules for selecting the President of the Court, as well as provisions related to the execution of judgments of the Court.