Sooner or later all integration associations using mechanisms of supranational legal regulation, decision-making process and execution face problems of constitutionalization. They need to build a coherent and consistent system of relations between supranational, intergovernmental and national authorities, between supranational and national sources of law. They need to overcome the obstacles that lie in the way of building a common economic space, to remove the contradictions caused by the need to ensure the four basic freedoms of the common market. Constitutionalization provides both the theoretical basis and the necessary tools. The European Union first encountered this problem. He followed the path of hierarchization of relations and law. The European Union has formed a separate legal system giving the internal legal order of association a set of qualitative characteristics that are considered to be classical to some extent. Priority attention was given to the development of fundamental values that are now of a high importance for the EU and to the gradual promotion of the legislative process to the forefront of such a supranational body as the European Parliament. The experience gained by the EU in this area can be of great benefit to the Eurasian Economic Union that is also formed according to the patterns of supranational institutional and legal construction. This experience is of particular importance in view of the crisis experienced by the EU since only the EU was able to develop institutional and legal solutions that can work within the framework of the integration association and which should be discarded. The article shows that the EAEU differs from the EU in a wide range of parameters, its goals and principles of functioning. It argues that the recipes of constitutionalization in the form they were used by the EU it is not suitable for the EAEU. At the same time the technical tools of constitutionalization developed by the EU may be suitable for the EAEU to solve the current tasks of self-assertion, consolidation and positioning in the international arena.