Abstract Despite the significant academic interest in the economic cohesion, the various aspects of convergence and the ways they can be measured still remain theoretically unclear. These are issues of extreme political significance, especially for countries aspiring for EU and euro area membership. The goal of this paper is to consolidate a variety of theoretical views on the convergence and its measurement and use it as the basis to assess the progress and the current state of economic convergence to the EU of the four candidate countries. The interrelation between the three forms of convergence in the different phases of the economic cycle is studied and the slobs in the ways the convergence is measured are outlined. The study reveals large differences between the candidate countries in achieving convergence with the EU. Their experiences do not confirm the positive relationship between nominal and real convergence. The structural convergence considered as convergence of sectoral structure has but little impact on the real convergence.