The article analyzes how global socio-political destabilization manifests itself, and how this is associated with the growing inefficiency of many international institutions due to an increasingly dysfunctional “unipolar” world order model. By focusing on the examples of the EU and the Russian Federation, this article studies the influence of global destabilization on the dynamics of political institutions both on the level of individual states and on the supranational level. Some general characteristics defining the modern political and institutional dynamics across EU countries are analyzed; these are associated with processes for strengthening socio-political destabilization. These trends, in particular, include: the decline in the effectiveness of traditional political parties, the growing polarization of party-political systems; the rise of populism, euroscepticism and right-wing radicalism; intensified contradictions in interactions between central and regional political institutions, amidst the growth of separatist sentiments; and the collapse and fundamental transformation of the structure and functions of the national state (nation-state) as an “ideal”. It is shown that the supranational political institutions of the EU as a whole are not effective enough in responding to the new challenges of external cultural migration, political polarization within European societies, the crisis of the social state, and the global COVID-19 epidemic. The reasons for this inefficiency are analyzed. In Russia, which is yet to fully take the form of a Western European-type nation-state, the political institutions introduced in the 1990s are undergoing intensive changes, adapting to this global destabilization in accordance with the model of institutional tracks that is different from the model of the national state. This involves applying elements of an imperial socio-political organization. Therefore, the first part of the study is devoted to the analysis of the problems and symptoms of increasing global destabilization and the formulation of the research problem; this is then solved in the next three parts. In a comparative perspective, three cases of institutional dynamics were studied: the EU as a whole, the EU at the level of national states, and the Russian Federation as a paradoxical state (national in form, but evolving in a different direction). The final part discusses the results and main findings of the study. From 2020 to 2030, as the EU and Russia are entering a period of deep and critical institutional, it is predicted that they must transform and adapt to the upcoming dramatic remodeling of the world order.