The paper estimates a model for the real U.S./U.K:. exchange rate. The Kalman filter is used to identify a permanent and a transitory component. We find the variance of the transitory component shifts among three states according to a Markov-switching process. The model is estimated by Gibbs sampling. The transitory component appears to be driven by temporary monetary phenomena. The shifts of variance occur at times of historically significant monetary events. We find the permanent component is cointegrated with relative per capital income levels, as in the Balassa-Samuelson hypothesis. The data support a model that contains a transitory component driven by monetary phenomena and a permanent component driven by relative income levels.