Convergence theory holds that as states develop, they tend to show increased similarities in attitudes and characteristics. Convergence is of great importance within the European Union, as achieving its cohesion requires the convergence of states at all levels, economic, social, administrative, and institutional. The literature has dealt extensively with the investigation of the possible convergence of European countries in several areas. The present study aims to investigate the possible

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... gence between the 28 countries of the European Union in the field of crime, for the period from 2003 to 2018. In addition, the possible existence of a "natural rate" of crime in the categories of crimes was investigated. The hypotheses of σ and absolute β convergence between states were used, as well as the Dickey-Fuller unit root test to investigate the existence of stationarity in the data time series of each state. The empirical analysis did not reveal the existence of a "natural crime rate". Of the categories of crimes included in the analysis, statistically significant β and σ convergence between EU states was found only for that of homicides. In the other three categories of crimes, no significant signs of convergence β and σ were found. Finally, in the three additional variables that were analyzed and related to the characteristics of the national criminal justice and public order systems, there were indications of convergence between the states.