This paper introduces an efficient estimation for fractional cointegration models which capture long run economic equilibrium relationships while allowing for a wider range of mean reverting behavior than standard cointegration analysis. The Fully-Modified method which is suggested in Phillips and Hansen (1991) can be applicable to fractional cointegration models to reduce second order biases. The comovement of nominal exchange rates is analyzed in a fractional cointegration models. Exchange rates dynamics are estimated by the efficient estimation method. Empirical results based on data for the 1957-1997 period show that there exists a cointegration relationship in a group of exchange rates.