The positive link between good institutions and economic development is well documented in the literature on the deep determinants of economic growth. Consequently, convergence in institutional quality should be a necessary precondition for income convergence; however, only recently, researchers started to investigate empirically the nature of institutional development. This topic seems to be of particular relevance for the European Union (EU) since convergence in institutions and in per capita income across the EU Member States are key goals of the European integrations process. Especially in the course of the various EU enlargement waves starting in 2004, it was intensively discussed whether institutional and structural homogeneity are necessary preconditions for real convergence and the smooth functioning of the EU or whether a (further) catching up in the institutional and economic development will endogenously occur after the EU accession. Our paper is dedicated to the analysis of these institutional dynamics within the EU. In particular, we analyze the formation of institutional convergence clusters using Phillips and Sul’s (2007, 2009) log t test over the period 2002 to 2018. It is the first study that takes into account the possibility of multiple equilibria when analyzing the institutional catching-up process within the EU, whereas previous contributions focused on the empirical concepts of beta- and sigma-convergence. Our results indicate the existence of multiple institutional clubs (for the dimensions government effectiveness, regulatory quality, rule of law, and control of corruption of the Worldwide Governance Indicators) with various countries being stuck in a poor institutional trap. Moreover, we find that institutional convergence clubs are formed mainly on the basis of geographic region. Northern and Western European countries are typically in the higher institutional clubs whereas the lower institutional clubs comprise primarily Eastern and Southern European countries. When analyzing per capita income clubs, a rather similar picture emerges, suggesting that the underlying institutional clusters determine the formation of income clubs. Among the countries that joined the EU after 2004, Estonia, Lithuania, and Latvia perform best with respect to their institutional catching-up, whereas most of the remaining new member countries are found to be stuck in poor institutional traps. The situation is particularly severe for Slovakia, Slovenia, Bulgaria, Croatia, and Hungary. We also study the factors that determine club membership by using an ordered probit model. Most importantly, we find that the initial levels of human capital and institutional quality are decisive for determining whether a country is on a high or low institutional growth path.