We apply the Range Unit-Root (RUR) test, a new nonparametric test advanced by Aparicio et al. (2006), to the exploration of stationarity for 19 Asian-Pacific currencies. The RUR test is exceptionally well suited to this analysis because it is robust against multiple structural breaks, parameter shifts and certain additive outliers, does not depend on the variance of any stationary alternative and thereby outperforms standard tests in terms of power on near-unit-root stationary time series. We find strikingly favourable results for trend-stationarity for most of the 19 Asian-Pacific currencies studied. Our results indicate that the long-run equilibrium Real Exchange Rate (RER) varies with changes in some real economic factors, hinting at some type of Balassa–Samuelson effects, which is particularly plausible for export-led, fast-growing economies such as many of the Asian-Pacific countries included in this study.