The article discusses the influence of proportionality theory, which explains the existence of a "third space" between politics and law and the integration of the states of the Eurasian Economic Union (EAEU) in the philosophy of international law. Taking into account the modern judicial and contractual practice, the issues of building a single legal space, training lawyers on the EAEU law, the advantages of using the "second mode" method, the role of the Court of the EAEU, etc. are analyzed. The author reveals the problems connected with the strictly normative understanding of the EAEU law, the non-recognition of the properties of supremacy and direct action behind this law, the inefficient position of the EAEU Court, "towing" the harmonization of the national legislation of States, undeveloped international cooperation with other subjects of international law, preventing the construction of the "third space". Using the approaches of representatives of the school of "integration through the law", a number of solutions to these problems are proposed. In particular, it is proposed to develop a unified concept of teaching the discipline "The Law of the EAEU", and introduce it into the educational programs of legal universities and faculties not only in Russia, but also in other EAEU States.