This paper considers some of the main long-run equilibrium relationships in international linance. We supplement the Phillips-Perron test. which has a unit root under the null. with the new KPS test statistic which is based on a stationary null and apply them to the various exchange rate fundamentals. The application of the Jahansen test for multiple cointegrating factors finds evidence of the existence of stable money demand functions in both the USA and UK with relatively short-lived perturbations. However, there appears to be insuffkient information in the data to distinguish & hether the real exchange rate has a unit root or is persistent and mean reverting. The consequent persistent deviations from purchasing power parity appears the only source of rejection of the equilibrium monetary model.