This paper proposes a flexible theoretical framework to assess the conditions under which long-run comovements are likely to appear between exchange rates. We introduce a three-country extension of the Taylor rule fundamentals model with adaptive learning. Moreover, economies are affected by common and/or country-specific shocks and react according to the preferences of central banks. The simulation results suggest that the extent to which exchange rates comove in the long run strongly depends on the extent of linkages between economies and the purchasing power parity of exchange rates. Indeed without similar Taylor rules in two economically linked countries, exchange rates comovements disappear. We pursue our theoretical analysis using real data and find strong evidence of fractional cointegration between several European exchange rates.