In this paper we examine whether the Markov switching (MS) models and exponential smooth transition autoregressive (ESTAR) nonlinear models can give any additional insights into real exchange rate behaviour during the period 1974-1998. The results from MS models show that there are clearly long swings in the real exchange rate series, which can be characterize as a depreciation regime and an appreciation regime. Furthermore, the regime staying probabilities are relatively high, although the process is eventually mean reverting. The ESTAR model results implies random walk behaviour for small deviations from PPP and fast adjustment for large deviations, which are in line with the MS model