The objective is to determine the perspectives of the cooperation of the Russian Federation and the European Union (EU) Member States in frames of the 1980 Convention on the Civil Aspects of International Child Abduction. The article used scientific approach that facilitates identification the main aspects and concepts of the study. The research used scientific methods of cognition, i.e. analysis, dialectics and synthesis, the generalization and system-structural method and practiced special methods of science such as: legal and technical, historical and forecasting methods. The authors conclude that the acceptance of a third country’s accession to the 1980 Convention falls under the exclusive external competence of the EU, thus, the EU Member States are not competent to decide the issue of accepting of accession of third State. In this case in accordance with the EU Council decision of October 6, 2015 authorizing EU Member States to make a statement, in the interests of the EU, on the acceptance of accession of the Russian Federation, it is clear that the acceptance of accession of Russia to the 1980 Convention by EU Member States is not connected with their distrust of the legal system in Russia. Russia is steadily moving towards ensuring transparency in the implementation of the 1980 Convention in order to stimulate the Member States to accept Russia's accession to the 1980 Convention even more actively. Results of the research can be used in the further theoretical developments in the field of international human rights law and be applied by the competent Russian State authorities involved in the realization of the 1980 Convention on the Civil Aspects of International Child Abduction. © 2017, by ASERS® Publishing. All rights reserved.