This study aims to examine the absolute and conditional convergence across the 27 EU Member States. To examine the absolute β convergence was used Baumol model (1986) estimated by OLS and Panel Data, and to examine the absolute σ convergence the Quah model (1993) by graphical analysis. Subsequently, we analyzed the conditional convergence, also estimated by OLS regressions and Panel Data. Finally, we performed a cluster analysis with the aim to understand the differences between different schools of economic growth thought. With this work we conclude that there is absolute β convergence in general, but the absolute convergence σ occurs only in the 12 most recent member states. The conditional convergence is verified in general and with a top speed of convergence β absolute. Finally we conclude that the neoclassical school, since 1980, proves to be important for economic growth and convergence of the EU as the school Neo Schumpeterian just proves to be important since 1991. ; Convergence, absolute convergence, conditional convergence, economic growth