In this paper we use a Threshold AutoRegressive (TAR) model to capture the nonlinear dynamics of monthly real effective exchange rate data for the G7 countries. The novelty of our approach relates to the use of the real interest differential as the switching variable. This choice allows us to consider jointly the nonlinearity and nonstationarity issues using recent advances in asymptotic theory. We find that the null of linearity is easily rejected against the nonlinear model for all currencies considered. Further, for five out of the seven countries, where the null of unit root is rejected, we report evidence of quite rapid mean reversion.