We utilize non-linear models to examine the stationarity of oil prices (Brent, Dubai, WIT and World) over the period 1973:2-2011:2. Real oil prices are calculated and expressed in the domestic currencies of seven Asian countries (Indonesia, Japan, Korea, Malaysia, the Philippines, Singapore and Thailand) and in the U.S dollar. Applying linear unit root tests with and without structural breaks shows very limited evidence of stationarity. However, applying non-linear models shows evidence of non-linearity in all the cases. In most cases, we find significant evidence of exponential smooth transition autoregression (ESTAR) type non-linearity. Notably, the results for Japan suggest logistic (LSTAR) type non-linearity for the four oil prices. Applying unit root tests, which account for two types of non-linearities (smooth transition and nonlinear deterministic trends), reveals evidence of stationarity in all the cases.