The appreciation of the dollar in the aftermath of the euro launch came as a surprise to most observers; furthermore, the traditional models fail to capture its dynamics. Is this a confirmation of Mussa's, Meese's and Rogoff's results, according to which no structural model can perform better than a random walk? More optimistically, this study shows that a structural VAR model of the Mundell-Fleming type satisfactorily explains the behaviour of the euro and its relationships with the fundamentals. My estimates indicate that dollar appreciation is primarily due to the cyclical strength of US demand. By contrast, they do not support the often-voiced theory that dollar appreciation is to be accounted for with the "new economy." Finally, the model shows that monetary shocks have limited effects on the exchange rate and very strong effects on inflation. This justifies the emphasis placed by central banks on the pursuit of internal objectives rather than exchange rate stability.