The European Union has become an important shaping factor in international relations, but how and under what conditions it can exercise influence and contribute constructively to global order are still not well analysed. In fact, the EU's contribution may resemble more that of a force in physics than of a great power in the traditional sense of international relations (which the EU is not, and will not become in the near future), and its influence depends probably more on what the EU represents and how well it manages its own realm, rather than on what it can do externally. In this sense, European influence in international relations presently benefits from past achievements, and may therefore have peaked if the twin challenges of enlargement and national structural deficiencies are not addressed effectively. But even if the European Union does master those challenges successfully, and thus manages to sustain and perhaps even enhance its influence as a force in international relations, it will still have to proceed cautiously and clearly focus its attempts on shaping its external environment and contributing to a ‘concrete’ or ‘civilized’ global order. In a global setting that, despite appearances to the contrary, seems characterized by a diffusion rather than a concentration of power and by strong tendencies towards entropy rather than order, the EU can and will probably not remain America's principal ally in sustaining Pax Americana. Nor does it seem likely to become an equal partner in a constructive, balanced transatlantic relationship, let alone a great power capable of challenging, perhaps together with others, America's apparent pre-eminence. The most plausible assumption for the EU's future role in the new balance of global order is that of a ‘civilian force’ with a regional focus. It may best be able to contribute to global order by managing its own realm well, promoting the normative and institutional infrastructure for civilized international relations, not least in the sense of functioning statehood, and working towards effective multilateralism.