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Using annual data spanning two centuries for dollar-sterling and franc-sterling real exchange rates, we find strong evidence of mean-reverting real exchange rate behavior. Using simple, stationary, autoregressive models estimated on prefloat data, we easily outperform nonstationary real exchange rate models in dynamic forecasting exercises over the recent float. Such stationary univariate equations explain 60-80 percent of the in-sample variation in real exchange rates, although the degree of short-run persistence may be high. The econometric estimates imply a half-life of shocks to the real exchange rate of about 6 years for dollar-sterling and a little under 3 years for franc-sterling.