The entry ticket for the Economic and Monetary Union and for adopting the single currency is obtained when an EU member country achieves the five nominal convergence criteria stipulated in the Maastricht Treaty. Since the launching of the euro on 1 January 1999 by 11 European Union member states, another five countries joined the euro. Out of the 27 EU countries currently only 16 Member States have adopted the euro at most recent case in this regard is Slovakia on 1 January 2009. This means that 11 states have not yet adopted the euro and are fully participating in the third stage of the economic and monetary union. The idea of this paper appeared amid the advance preparation of the Eastern block countries in the European Union to the admission to a higher stage of integration. After analyzing the status of compliance with the convergence criteria of the Eastern bloc countries in the EU, of Romania in particular, we came to the conclusion that Romania does not comply with any of the criteria for adopting the single European currency, with all the progress made in terms of European integration, so it is shown that efforts must be intensified in order to achieve a high degree of sustainable convergence. This effort is aimed at making and maintaining price stability in a sustainable manner, as well as reducing the large deficits incurred during the financial and economic crises, in some Member States and to achieve and maintain an optimal level of the public finances.