The stability of inflation differentials is an important condition for the smooth working of a currency area, such as the European Economic and Monetary Union. In the presence of stability, changes in national inflation rates, while holding Euro-area inflation fixed contemporaneously, should be only transitory. If this is the case, the rate of inflation of the whole area can also be interpreted as a predictor, at least in the long run, of the different national inflation rates. However, in this paper we show that this condition is satisfied only for a small number of countries, including France and Italy. Better convergence results for inflation differentials are, instead, found for the USA. Some policy implications are drawn for the Eurozone.