Under certain conditions, efficient markets imply random walk behavior in real exchange rates. Much of international finance theory, however, is based on the idea of purchasing power parity, which implies mean reversion in real exchange rates. This paper uses variance ratio statistics to test for random walk behavior in real exchange rates. Unlike most previous tests of this hypothesis, the tests do reject a random walk for monthly data; however, the monthly statistics do not provide evidence in favor of mean reversion. Interestingly, tests using annual data for the twentieth century are unable to reject a random walk despite evidence of mean reversion. This appears to be due to the relatively small number of observations available.