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When some European country willing to aspire to the membership in the Eurozone, at first it must cover the Maastricht convergence criteria, which are divided into fiscal (government deficit, public debt) and monetary (price stability, exchange rate stability, stability of long-term interest rates). The basic requirements for criteria were settled at the time of their formulation in the Protocol to the Treaty of European Union. There was the requirement to ensure a high degree of sustainable economic convergence. Currently, global uncertainty and significant financial fluctuations in the world and off course in Europe, appears to be important question of whether the fulfillment of these nominal criteria is sufficient condition, for the adoption of the common European currency as a guarantee of future success Eurozone membership. The basic objective of the article is through the analysis of monetary convergence criteria - price stability - to assess the merits of sustainability monetary criteria in selected European Union countries. We concluded that it is a certain distortion ability to express reference value determined by developments in the EU member states (and not members of the Eurozone). However, it should ensure price stability as a precondition for the smooth functioning of the euro area, covered by a common monetary policy of the ECB. [ABSTRACT FROM AUTHOR]