This paper employs a panel unit root test for the real exchange rates of 13 EU member countries. The estimation period covers the EMS period from 1980:1 to 1992:2 In contrast with the earlier panel unit root studies concerning purchasing power parity (PPP), effective real exchange rates are used. As a result, the non-stationarity of the real exchange rate was rejected. However, the half-life of the real exchange rate adjustment turned out to be long. Potential reasons for this might be the relatively short estimation period and the nature of the data.