This paper analyses the time series behavior of the components of the real exchange rates between the founding member states of the EMU before and after the start of the EMU. Various panel and univariate country-specific tests show that the levels of these components are typically random walks. The resulting real exchange rates are also random walks and their components are not cointegrated. It is argued that these results question the operability of the EMU under the current policy regime in the long-run. One possibility to deal with this problem could be the suspension of the principle of a “single monetary policy”: