Since 2004 and the enlargement of the EU to new Central and Eastern Europe members, Russia seems to be at odds with the growing attraction of EU membership in the former Soviet region, and even in the former Soviet Republics. The enlargement process has not found its limits yet, and could attract newly independent States, like Ukraine or Georgia. The EU is also showing some interest for « frozen conflicts » in Abkhazia, South Ossetia, Transnistria or High Karabakh. All these developments could push Russia towards a defensive policy, in order to avoid marginalisation. Yet, Russia actually needs peaceful relations with the EU, which is both its first commercial partner and its first investor. The EU needs hydrocarbons from Russia as well, and its attraction is more of an objective nature than the product of an organised power policy. In this context, any tension between Russia and the EU would result in a zero sum game. Their cooperation, in their bordering regions, should be seen as positive for both of them.