An expected relative PPP model, augmented by elements of a monetary model and byexternal influences, is used to track the path of the Euro-Dollar rate since the inception ofthe European currency. A similar model is also applied to the estimation of the Rupee –Dollar exchange rate. Expected inflation rates, based on a specified formation process,are, indeed, seen to be significant determinants of the Euro exchange rate. While moneysupplies are not significant, interest rate differentials do matter; higher real Euro areainterest rates appreciate the Euro. US government budget deficits appreciate the Dollarwith a lag, presumably due to financing capital inflows, but current account deficits donot have a perceptible influence in the period of the study. Oil price increases and higherinternational reserve holdings in major Asian markets, which may be skewed towards thedollar, also have no discernible impact on the Euro-Dollar rate. For the rupee – dollarrate, interest rate differentials and inflation differentials work well as predictors. Higherinterest rates relative to the global rates appreciate the rupee, i.e., the rupee – dollar ratefalls. Higher expected inflation in India depreciates the rupee. Current account surplusesare seen to appreciate the rupee, but investment inflows function poorly as a predictor. Arandom walk model may work as well as a formal monetary – PPP model in forecastingthe rupee exchange rate.