In order to effectively regulate the circular economy (CE) at the national and international levels, it is essential to have a unified and informative system of indicators for monitoring the progress in the CE. The lack of standard indicators for measuring the progress of cyclicality leads to contradictions and misunderstandings, which is a problem for the implementation of CE strategies. This paper aims to adapt dynamic clustering approaches to solving strategic management problems of circular production and consumption processes. To achieve this goal, the authors performed the following tasks: (1) tested clustering algorithms by ranking EU countries by the level of development of the circular economy; (2) identified the approach that allows the best classification of EU countries, considering changes in the indicators of the level of CE development in 2000–2019 (dynamic classification); (3) developed a software module using python libraries to classify and visualize the results. The results illustrate that the k-means algorithm has a good discriminatory ability in division of all countries of the training sample (EU countries) into several clusters with different dynamics in the development of the CE. The best quality of classification is obtained by the indicator “Generation of municipal waste per capita”; satisfactory quality of the classification is obtained by the indicator “Generation of waste excluding major mineral wastes per GDP unit”. The study results demonstrate the fundamental applicability of the object-oriented and classical statistical approach to solving strategic management problems of the CE and their potential effectiveness in terms of the clarity and information content of reflecting cyclical processes