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Equilibrium models of real exchange rate determination in the presence of transactions costs imply a nonlinear adjustment process toward purchasing power parity (PPP). Conventional cointegration tests, which ignore the effect of transactions costs, may be biased against the long-run PPP hypothesis. The authors' results, using both monthly data for the interwar period and annual data spanning two countries, clearly reject the linear framework in favor of an exponential smooth transition autoregressive process. The systematic pattern in the estimates of the nonlinear models provides strong evidence of mean-reverting behavior for PPP deviations and helps explain the mixed results of previous studies. Copyright 1997 by the University of Chicago.