The stability of a taxonomy algorithm against minor changes in a data set (e.g. subtraction from a dataset, small changes in variable values) or algorithm parameters (e.g. random selection of parameter values) is a desired property of the method. There is an opinion in the literature that, when properly selected, multiple uses of a given algorithm should give rise to little or no difference in the final clusters (i.e. it should give stable results) and reveal the actual structure present in the data. This criterion is particularly applicable when selecting the number of groups (parameter k). The purpose of the paper will be to examine the stability of grouping the EU countries in terms of sustainable development levels.