Structural models of the exchange rate have performed very poorly for the industrialized nations during the post-Bretton Woods period. A number of studies found that the out-of-sample forecasts of structural models are no better than those of the random walk model. This result is readily explained if the fundamental determinants of exchange rates (e.g., money supplies, income levels, and interest rates) are themselves near-random walk processes. However, some studies provide evidence that there are no cointegrating relationships between bilateral nominal exchange rates and the so-called fundamentals;One aim of this research is to estimate a structural exchange rate determination model. To this end, the Johansen cointegration technique is used to re-examine the existence of cointegrating vector(s) between the exchange rate and the supposed fundamentals;The second aim of the research is to propose a modelling strategy for models with cointegrated variables. In that regard, each cointegrating vector is viewed as either a behavioral or a reduced form equation stemming from a structural model. Identification of the behavioral equations can be facilitated by the imposition of zero restrictions on the cointegrating vector(s). Given that these equations represent long-run static properties of the data, a more complex dynamic structure can be derived combining this prior analysis to the system. This can be achieved by using conventional innovation accounting (variance decomposition and impulse response functions) techniques based on the error-correction representation;We apply the procedure to estimate a structural model of the French Franc/U.S. Dollar and Italian Lira/U.S. Dollar exchange rates. Using quarterly data from the post Bretton Woods period, we find multiple cointegrating vectors which we identify as (1) the money market equilibrium relationship(s) and (2) the modified Purchasing Power Parity (PPP) relationship consistent with the Dependent Economy Model of exchange rate determination. We also estimate the error-correction representation (with the restricted and unrestricted equilibrium errors) in order to characterize the short-run properties of the system. Using conventional accounting techniques, we show that a reasonable proportion of exchange rate variability is explained by the fundamentals.