It is well documented that real exchange rates between the United States and many industrialized countries in the post-Bretton Woods period are integrated. This result implies that purchasing power parity (PPP) does not hold even as a long run relationship. This paper demonstrates that the failure to reject the unit-root hypothesis may result from the low power of existing univariate test procedures. I test for unit roots in real exchange rates by employing a more powerful panel-based procedure. Using both CPI and WPI real dollar exchange rate data, I strongly reject the null hypothesis of a unit root. My results provide overwhelming support for the long-run PPP under the current float. Copyright 1996 by Ohio State University Press.