Using a neo-classical growth model, we analyse the real and nominal GDP per capita convergence of 21 emerging market economies (EMEs) of Central and Eastern Europe towards the EU15 average by 2050. We estimate the countries initial capital stocks and project future investment as a function of the GDP per capita gap, among other things, in order to have converging physical capital intensities in the long run. Due to standard-convergence in the model, catching up will continue at a decelerating speed. Also nominal convergence in prices that will lead to a real appreciation of the EME currencies with respect to the euro is projected as a function of the GDP-per-capita gap vis-à-vis the EU15. We also discuss whether the level of human capital in the EMEs is likely to allow for full catching up. We argue that the EU membership of most of the EMEs is likely to improve their economic, investment and business environments and lead to economic and other policies that support long-term convergence. According to the results, the EMEs will not quite catch up with the EU15 by 2050. However, our analysis of the uncertainty related to the growth rates and calculations of a confidence band for the results, as well as a qualitative assessment of other factors (politics, institutions, human capital) that have not been taken into account in the model explicitly lead us to conclude that some of the EMEs are likely to catch up with the EU15 average during the course of the next couple of decades.