In today’s world, there is intense competition between integration entities that are working to strengthen and expand their political and economic positions. This article examines the movement of the Eurasian Economic Union in this direction. Aim. To propose a way to ensure a common legal space in the Eurasian Economic Union. Tasks. To analyse the regulation in force in the Eurasian Economic Union on the execution of court judgments and arbitral awards, to identify problems that member states of the Eurasian Economic Union may encounter in the execution of court judgments and arbitral awards. Methods. In this work were used both general scientific methods of knowledge: analysis, synthesis, generalization, and particular scientific methods: formal-logical, formal-legal, comparative-legal, method of legal prediction. Results. One of the most acute problems faced by states in the execution of judicial and arbitral decisions is the problem of execution of annulled judicial or arbitral decisions. To prevent this problem within the European Economic Union, the author considers that the members of the European Economic Union should not accede to the Convention on the Recognition and Enforcement of Foreign Judgements in Civil or Commercial Matters of 2 July 2019, as it does not resolve the fate of annulled judgements. With regard to arbitral awards, it would be desirable for the Member States of the European Economic Union to conclude between themselves a protocol to the Convention on the Recognition and Enforcement of Arbitral Awards of 10 June 1958, which would exclude the enforceability of annulled arbitral awards in all the States parties to the Protocol. The drafting of this additional protocol could be entrusted to the Eurasian Economic Commission of the European Economic Union. Conclusions. The Eurasian Economic Union needs to create a predictable legal space, which would primarily be ensured by the free movement of judicial and arbitral decisions. Keywords: eurasian integration, international commercial arbitration, enforcement of judgments, enforcement of arbitral awards, setting aside an arbitral award.