In the previous decades, the European Union (EU) has succeeded in integrating new member countries, in economic and in political respects. Three main reasons lie behind this successful integration process: First, the solidarity of richer EU members with their poorer counterparts, second, the effectiveness of the integration policies conducted by the EU, and third, the willingness of new member countries to arouse and accomplish an economic catch-up process towards EU average levels. With the enlargement by ten new members in May 2004, the EU is facing the biggest challenge in its history. Thereby, the population of the Union will rise by 25%, while its overall GDP will increase by merely 5%. Apart from the economic problems that may emerge because of this discrepancy, further difficulties may arise because some of the new entrants are former centrally planned economies that have not yet completed their transformation processes towards free market-economies. In this paper, we want to investigate whether the Union may be moving towards a new era in the dynamics of integration. In doing so, we will analyze some of the main challenges the EU will be confronted with in the near future. In detail, we have identified two types of challenges. On the one hand, these are internal challenges, being closely related to the structural adjustments of the Union. We will further differentiate these internal challenges into economic and political ones. On the other hand, there exist external challenges that predominantly concern the competitiveness of European countries in a global context. With regard to these external challenges, we will only deal with economic aspects. One of the main findings of our analysis is that the EU will have to manage a highly difficult trade-off between the stimulation of Union-wide economic convergence and international competitiveness of its member countries. In the short-run, the process of European integration can well be deepened, given that the current controversies with regard to the financing of European support programs for poorer members and with regard to the implementation of a new constitution for the EU will be resolved. In the long-run, even if these controversies can be remedied, it appears likely that the dynamic process of European integration will not proceed as smoothly and as successfully as it did in the past. That is because the economic disparities across EU member countries have never been larger, and because the "development funds" now need to be distributed among a larger number of countries than in the past. Apart from these difficulties, it can be expected that the concentration on intra-European integration processes will be harmful to the international competitive strength of the entire Union, especially when this colossus confederation fails to take account of the economic desires of its strongest members. Certainly, the strongest nations within the Union are exposed to the pressures of international competition among highly developed nations on the basis of innovation and productivity. This kind of competition can be described as a Schumpeterian competition. In the light of all these aspects, there are indications that a European Union of "two velocities" will emerge, whereby a core of countries will mainly pursue the objective to strengthen their international competitiveness, while the remaining members will be struggling to accomplish an economic catch-up process to intra-European standards.