After presenting the institutional construction during the pre-accession and post-accession to the Economic and Monetary Union (EMU), the exchange rate mechanisms (ERM) in several countries and the convergence criteria, we go on with a brief analysis of the way the CEE countries cope with the convergence criteria in accordance with the Maastricht Treaty. Then, the study deals with a topic often discussed in the scientific literature and included on the agenda of decision-makers at various levels, in order to clarify the following major issues: a shorter transition to the euro, the exchange rate equilibrium versus the inflation rate diminution and the Balassa-Samuelson effect, the exchange rates and the exchange rate deviation index, evidences concerning the real exchange rate equilibrium and the appreciation of the exchange rate in the CEE countries.