The article contains proposals to the Commercial Procedure Code of Ukraine, Civil Procedure Code of Ukraine, Code of Administrative Procedure of Ukraine in part of international commercial arbitration, which may be used by the legislator for the purposes of improvement of procedural legislation after the entry into force of a law based on draft Law № 6232 On Amendment of the Commercial Procedure Code of Ukraine, Civil Procedure Code of Ukraine, Code of Administrative Procedure of Ukraine and Other Legislative Acts. Basing his findings on the doctrinal research, the author suggests to implement to the procedural codes a mechanism of stay of court proceedings pending consideration of another case, which is being considered by an international commercial arbitration tribunal. The author also suggests to vest courts with discretionary powers to stay court proceedings pending the entry into force of a decision of a court on the recognition and enforcement of a foreign arbitration decision or on the refusal to grant its recognition and enforcement (or issuance by the court of a final decision as a result of the consideration of a claim on the annulment of a commercial arbitration award — for arbitration awards issued in Ukraine). The article also sheds light on the non-advisability of the implementation to the procedural codes of a provision, in accordance to which circumstances established by the award issued by an international commercial tribunal shall be established de novo during the consideration of other civil, commercial and other cases involving the same parties or a person, in whose respect such circumstances have been established.