Economic disparities between the regions of the European Union are of constant concern both for policy and economic research. In this paper we examine whether there are overlapping trends of regional development in the EU: overall convergence on the one hand and persistent or even increasing spatial concentration (agglomeration) on the other. Kernel density estimation, Markov chain analysis and cross-sectional regressions provide evidence that convergence of regional per-capita income in the EU15 has become considerably stronger in the 1990s. The reduction of income disparities, however, is a phenomenon between nations but not between regions within the EU countries. European integration (and possibly European regional policy) foster the catching-up of lagging countries but at the same time forces for agglomeration of economic activities tend to increase disparities within the EU member states. Obviously, the productive advantages of spatial proximity do not vanish in the knowledge economy.