This paper examines the significance of different fundamental regimes by applying various monetary models of the exchange rate to one of the politically most important exchange rates, the exchange rate of the US dollar vis-à-vis the euro (the DM). We use monthly data from 1975:01 to 2007:12. Applying a novel time-varying coefficient estimation approach, we come up with interesting properties of our empirical models. First, there is no stable long-run equilibrium relationship among fundamentals and exchange rates since the breakdown of Bretton Woods. Second, there are no recurring regimes, i.e. across different regimes either the coefficient values for the same fundamentals differ or the significance differs. Third, there is no regime in which no fundamentals enter. Fourth, the deviations resulting from the stepwise cointegrating relationship act as a significant error-correction mechanism. In other words, we are able to show that fundamentals play an important role in determining the exchange rate although their impact differs significantly across different sub-periods.