Abstract: Enforcement of arbitral awards in foreign countries is carried out on the basis of the Convention on the Recognition and Enforcement of Foreign Arbitral Awards of June 10, 1958 (the 1958 New York Convention). Provisions of the New-York Convention of 1958 are rather laconic and some of them cause difficulties in enforcement. Such a provision is subparagraph (e) of Article 1 of the 1958 New York Convention. «å» of paragraph 1 of article V, which provides for the possibility to execute an arbitral award annulled at the place where it was rendered. Similar norms are provided for in the Russian legislation. Using general scientific methods of knowledge (analysis and synthesis, induction and deduction, generalization) and special scientific methods (formal-logical, formal-legal and method of legal forecasting) the analysis of execution of annulled arbitral awards in foreign countries was carried out. Scientific novelty of the present research consists in substantiation of the fact that the arbitral award and the acts adopted in respect of this award form a single totality, each element of which should be taken into account in the enforcement of the arbitral award. It is found that the enforcement of the annulled arbitral awards is contrary to the purpose of the 1958 New York Convention and the logic of its provisions. The enforcement of such decisions also violates the rights and interests of the parties to the arbitral proceedings. It is proposed to amend the current legal regulation and to provide for a clear provision prescribing the refusal to recognize and enforce a foreign arbitral award that has been set aside by a State court in the place where it was made.