Issues of enforceability of court decisions are among the so-called “eternal” problems that require constant attention from both the legislator and law enforcers. This circumstance is largely due to the very nature of the judiciary and its decisions, the presence of special legal mechanisms for the execution of these acts, as well as the importance of the political will of specific subjects of relevant relations to implement the requirements formulated in court decisions. It is obvious that the significance of these factors increases markedly with an increase in the level of the court that makes the appropriate decision. As a result, the greatest difficulty with execution is observed precisely in relation to decisions of higher judicial instances. Meanwhile, due to the special constitutional status of these bodies, it is their practice of implementing decisions that have a significant impact on the national legal order and the legal system itself. Given the broad, complex nature of the relevant issues, the authors offer its analysis in the framework of a publication consisting of two parts, which are two relatively independent articles. This article focuses on the analysis of the socio-political and legal characteristics of the institute for the execution of decisions of the Constitutional Court of the Russian Federation (hereinafter referred to as the Constitutional Court of the Russian Federation), including in relation to the self-execution of these acts. Issues related to legislative, law enforcement, doctrinal characteristics of the existing mechanisms for the implementation of decisions of the Constitutional Court of the Russian Federation at the federal and sub federal levels, the need to improve them deserve independent attention.