||Regression analysis of the real convergence and its connection to nominal convergence through Balassa-Samuelson effect shows that the nominal convergence is not a sufficient condition for the process of lowering the dispersion between the 10 accessing countries and the average of EU-15 (as variables GDP per capita and price levels are considered). Maastricht criteria which represent nominal convergence are slowing down the ability of the poorer accessing countries to “catch up” and naturally converge in real variables to wealthier European countries. Convergence of inflation means eliminating of price level convergence which is implied by Balassa-Samuelson effect. As to the fulfillment of the nominal criteria, the greatest problems to the present accessing countries cause the fiscal criteria. According to the regression analysis of β-convergence and Balassa-Samuelson effect, the theoretical real appreciation of the exchange rates in the range from 1.6% to 4% at average hypothetical GDP per capita growth level of 2% to 5% per year should be expected. The results should however be treated with caution because there are other very important external factors as FDI boosting the GDP growth. As to the euro adoption strategy, the currencies of the countries should stay at ERM II for the minimal period – required 2 years. The recommendation is that the countries should not hurry with the adoption of common currency because it might be rather harmful than helpful to them. The setting up of the central rate will be crucial.