The Economic and Monetary Union is the co-ordination of economic, fiscal and monetary policies, and it was considered that by creating EMU, the obstacles to the creation of a single market and to stimulate political integration would be removed. In order for the country to become part of the euro area, it must meet the criteria set in advance, known as Maastricht criteria. There are four criteria for nominal convergence: the criterion of price stability, the criterion of government finances, the criterion of the stability of the exchange rate and the criterion of long-term interest rates. Nominal convergence is what is needed to enter the euro zone, while real convergence will show how much are the benefits and costs of joining the EMU are. The subject of this research is the convergent movement within the Economic and Monetary Union, and the objective was to explain the convergence criteria and their significance in the development of countries and EMU. The results of the conducted research have shown that there is no statistically significant linear relationship between GDP per capita in PPS and nominal convergence indicators, i.e. that there is no statistically significant linear effect of the nominal convergence variables on the variable GDP per capita in PPS, which suggests that nominal convergence does not lead to real convergence. By analyzing the nominal and real convergence indicators, both groups of countries, as well as the entire eurozone, achieved convergence in certain periods, but none of the indicators showed the existence of sigma convergence throught the observed period. The movement of standard deviations of the nominal convergence indicators of the old (EA(12)) and new (NMS(7)) member states is at approximately similar levels and the differences between them are reduced, while the difference between the real convergence indicator of these two groups of countries is still large, which leads to the conclusion that the euro area countries have a greater degree of nominal convergence than real convergence.