What can explain the persistent fluctuations observed in non-fixed exchange rates? We use a version of the Kareken-Wallace two-country overlapping generations model to explain this empirical phenomenon. The agents use an adaptive learning rule to forecast expected prices in both countries instead of having perfect foresight as in the original Kareken and Wallace model. There are different but constant speeds of adjustment in the two countries. The constant speed of adjustment combined with a small shock to the money supply in one of the countries creates swings in the exchange rate. This is illustrated in various computational experiments.