There are evidences that the actual global crisis affected the convergence process in EU. Generally, just new adhered countries were more affected by the actual crisis. Today all forecasts are suffering by uncertainty. Last time, economists, with their methods and models, are invoked for actual crisis, but real causes could be found in policymaker's actions and in public opinion's influence, as a rule focussed only on short or very short-term. However, the methods and predictive models that economists are using seem to be not adequate for the new situation, especially due to the large extension of the actual crisis, at its turn caused by the globalization phenomenon. For the post-crisis period, we are presenting some likely challenges both in the real economy and in economics. There are different opinions regarding how deep and how long the convergence process will be affected. Synthetically, the pessimistic authors are viewing the future economic dynamics as one of so-called L type or U type or W type. Coming from lessons supplied by standard economic growth theories (Ramsey model, Solow-Swan model, Mankiw, Romer, and Weil model, etc.) and by empirical evidences, we are considering the convergence in the level of income per capita as a result of structural changes in economy.