This article assesses the current state of competition between the dollar and the euro. It presents the issues related to the « strong euro » and the international role of the euro. Economics is of course mobilized to explain the exchange rate of the euro and its process of international diffusion. Yet, economic theory does not suffice to explain what has happened between 1999 and 2003. The behaviours of the Fed and the ECB should also be studied, as well as the political credibility of the euro zone in front of the American leadership. The euro has now become the second world currency after the dollar, which is still prevailing. If Europe reaches a political identity, a true bipolarisation of the international monetary system may arise. – Summary AFRI-2004