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• We study real GDP per capita convergence among the CEE-8 and their catch-up towards the old EU-15 member states during the period 1995–2017. • We use an innovative analytical framework of convergence testing proposed by Phillips and Sul that accounts for heterogeneity in technological progress across countries. • Our empirical results indicate that in the EU-15 no distinct convergent patterns exist. • There is convergence among the CEE-8 countries. • The hypothesis of the CEE-8 convergence towards the old EU-15 is rejected • The CEE-8 are converging towards two largest EU countries: Germany and France. The enlargement of the European Union in 2004 to include Central and Eastern European countries has revived the convergence debate. This study concentrates on the empirical investigation of real GDP per capita convergence between the CEE-8 and their catch-up towards the old EU-15 member states. The empirical study is based on the innovative analytical framework of convergence testing proposed by Phillips and Sul that accounts for heterogeneity in technological progress across countries. Our empirical results indicate that in the EU-15 no distinct convergent patterns exist. However, there is convergence among the CEE-8 countries. Moreover, the hypothesis of the CEE-8 convergence towards the old EU-15 is rejected. Nevertheless, the CEE-8 seem to be converging towards two largest EU countries: Germany and France. [ABSTRACT FROM AUTHOR]