In this paper, we have verified the convergence process in the EU in the period 2001 – 2013. The methodology of this paper is similar to that of Artis and Zhang (1997), Boreiko (2003), and Crowley (2013), who also focused on the European convergence process. This paper is based on the thesis that the convergence process is proven if the clusters are gathering in shorter squared Euclidean distances during the time, or, alternatively, if the distances between European Union economies and Germany are shorter. First, in order to perform the cluster analysis, the convergence criteria are identified (the choice of the criteria is based on optimum currency area). Second, with regards to the criteria, we conduct thirteen cluster analyses for every year of the period 2001 – 2013. From this perspective, we focus on the differences between the analyses' outputs during the time. According to our results, it is possible to draw the conclusion that the economic convergence process in the EU was not proven.