The monetary model suggests that nominal exchange rates between two countries will be determined by important macroeconomic variables. The existence of a cointegrating relationship among these fundamental variables is the backbone of the monetary model. In a recent paper,Rapach and Wohar (2002, Journal of International Economics) advance the literature by testing for linear cointegration in the monetary model using a century of data to increase power. They find evidence of cointegration in five or six of ten countries. We extend their work to the nonlinear framework by performing threshold cointegration tests that allow for asymmetric adjustments in two regimes. Asymmetric adjustments in exchange rates can occur, for example, if transactions costs are present or if policy makers react asymmetrically to changing fundamentals. Moreover, whereas Rapach and Wohar (2002) found it necessary to exclude the relative output variable in some cases to maintain the validity of their cointegration tests, we can include this variable as a stationary covariate to increase power. Overall, using their same long-span data, we find more support for cointegration in a nonlinear framework.