This paper measures the convergence or divergence of EMU inflation rates and industrial production by testing for the existence of fractional cointegration relations. The notion of fractional cointegration allows for long-term equilibria with a higher degree of persistence than allowed for in the standard cointegration framework. We investigate both inflation and industrial production of EMU countries beginning with the introduction of the common currency and including the financial crisis and post-crisis period. Core as well as periphery countries are included in the study. By modelling possible breaks in the persistence structure we find evidence of fractional cointegration as well as a lower persistence before the crisis and a higher persistence by less evidence for fractional cointegration during the crisis. A second break which indicates the end of the crisis can be found as well. In addition, higher inflation persistence can be found for periphery than for core countries.