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We estimate nonlinear time-series models of the deviations of the dollar–sterling and dollar–mark exchange rates from the level suggested by simple monetary fundamentals over the recent floating rate period. The estimated parameters are statistically significant on the basis of empirical significance levels generated by Monte Carlo methods and imply nonlinear mean reversion towards the monetary fundamental equilibrium such that the speed of mean reversion increases with the size of the deviation from equilibrium. The results are used to provide an illustration of the overvaluation and undervaluation of the dollar against sterling and the mark over the recent float.