There is a large literature that investigates whether or not real exchange rates are stationary in an attempt to unravel support for purchasing power parity (PPP). At best, the empirical results are mixed. This paper applies a unit root test that allows for a simultaneous structural break in the intercept and slope, shown by Sen (2003) to minimize power distortions, to examine PPP for 17 OECD countries. Our results on PPP are mixed. When the real exchange rate is based on the US dollar, evidence is found of PPP for only France, Portugal and Denmark. When the real exchange rate is based on the Deutschmark, we find evidence of PPP for Austria, Belgium, Norway, Spain, Netherlands, Switzerland, and Denmark.