One can provide numerous examples of complete and timely execution of decisions of constitutional justice bodies; however, there are instances when such decisions are ignored, when their implementation is unjustifiably delayed or when the efforts to nullify their legal force are taken through the adoption of rules similar to those that were held unconstitutional. The author of this article analyses the reasons of non-implementation of constitutional review acts and proposes different solutions to this problem. The author discusses the notion and legal nature of legal positions of the Russian Constitutional Court, their correlation with decisions of the Constitutional Court and the lack of a precise mechanism for their implementation in the course of law-making and law enforcement practices. The author examines different kinds of liability imposed for non-implementation of decisions of constitutional justice bodies and proposes establishing preliminary constitutional review and administrative liability. In doing that, the author examines foreign experience of the Republic of Kazakhstan, the Republic of Belarus, the Republic of Kosovo, the Republic of Albania, and the FRG. In conclusion, the author proposes certain options for improving Russian legislation, which include, inter alia, the adoption of a law on regulatory legal acts in the Russian Federation.