Research background: Recently in the context of taxonomy methods a lot of attention has been paid to the issue of stability of these methods, i.e. the answer to the question: do the groups that were created as a result of clustering really occur (the structure is stable), or did they appear accidentally.Purpose: The article is inspired by the Reviewers of the author’s previous publications on this subject and will be a summary of research to date which has followed two paths. On one hand, they recognize ways of measuring cluster stability proposed in the literature (e.g. Rozmus, 2017). On the other, they use these measures to cluster Poland among the EU members in terms of sustainable development level (e.g. Rozmus, 2019).Research methodology: The literature proposes a number of different ways for measuring stability. Theoretical considerations have also led to the development of computer tools for the practical implementation of the proposed ways to study stability. The practical tools are available within several R packages, e.g.: clv, clValid, fpc, which are used in this researchResults: The results, however, showed that different measures of stability lead to different results.Novelty: The innovation of this approach is the use of stability measures to such a problem (i.e. clustering EU members in terms of the sustainable development level). In addition, the article will report a synthesis and comparative analysis of the results obtained using various stability measures.