This article aims at analyzing the problem of real exchange rate appreciation and competitiveness in the EU's ultra-peripheral regions by the case study of La Reunion Island. After describing economic characteristics of this French overseas department, such as the large deficit of the trade balance, this article looks for explanation by calculating and examining the statistical properties of the Real Effective Exchange Rate (REER). Our results show that this rate is stationary around a trend and provides evidence of i) an appreciation of the REER, but ii) no permanent overvaluation of the currency. These two results can be explained by the economic catch-up of La Reunion characterized by gains in relative productivity, and by the dynamics of the terms of trade and a permanent increase in the transfers from metropolis.