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In this study, we propose a new unit root test procedure that allows for both gradual structural break and asymmetric nonlinear adjustment towards the equilibrium level. Small-sample properties of the new test are examined through Monte-Carlo simulations. The simulation results suggest that the new test has satisfactory size and power properties. We then apply this new test along with other unit root tests to examine stationarity properties of real exchange rate series of the sample countries. Our test rejects the null of unit root in more cases when compared to alternative tests. Overall, we find that the PPP proposition holds in majority of the European countries examined in this paper.