Regulatory legal acts are analyzed (draft Regulations on Prisons, 1788 Charter of the Society of Guardians of Prisons, 1819 Instructions to the caretaker of a provincial prison castle, 1831, General Prison Instructions of 1915, etc.) that regulate key aspects of the activities of bodies state authorities providing medical assistance to convicts. The article discusses the main directions of the formation and development of the medical care system for persons serving sentences in prisons of pre-revolutionary Russia. Considering the lack of direct competence of the EAEU bodies to adopt acts in the field of private international law is proposed to start the drafting of a regional international treaty on the law applicable to contractual obligations, as the most common type of private-law obligation in cross-border relations. It is concluded that the EAEU law system is at the stage of its formation, therefore such signs as a direct effect (including criteria for direct effect) and the supremacy of the acts adopted by the Union’s bodies are still insufficiently formalized and supported by the regulations and practice of the EAEU Court. In order to study this legal phenomenon, a comparative analysis with the law of the European Union is carried out. The EAEU law system is analyzed from the point of view of its supranational characteristics, namely: the supremacy and direct effect of the sources of law. The conclusion is substantiated that it is impossible to ensure practical implementation of the freedom of movement of goods, services, capital and labor without the convergence of conflict regulation of the member states. The article deals with the problem of improving the rules of private international law of the EAEU member states through their updating and harmonization.