On the eve of the financial and economic crisis of 2008/09, the European Economic and Monetary Union (EMU) could look back to a decade of remarkable macroeconomic stability. Somewhat surprisingly, though, inflation differentials across member states have been substantial and persistent, causing large cumulative changes in relative price levels. This paper presents a stylized theoretical model of a monetary union which demonstrates how persistent inflation differentials can arise from inflation inertia in conjunction with the loss of monetary control on the national level. The interaction of inflation and output dynamics which is at the core of the model generates a pattern of 'rotating slumps' (a term coined by Blanchard 2007b). A number of implications are derived from the model which shed light on the observed behavior of cyclical conditions and inflation rates in the euro area. The paper concludes that the monetary-fiscal framework of EMU does not pay adequate attention to the need of dealing with internal macroeconomic tensions within the euro zone.