We suggest that the real exchange rate between the major currencies in the post-Bretton Woods period can be described by a stationary, two state Markov switching AR(1) model. Based on the forecast performance, both in-sample and out-of-sample, we find that this model out-performs two competing models where the real exchange rate is non-stationary. We also find that the existence of different regimes, as in the Markov switching model, is consistent with the common finding of unit roots in the real exchange rate.