This study aims to identify significant differences between the countries of the European Union, follow the course of achievement of the convergence objectives, assess developments against specific common characteristics of the countries, and propose possible measures that could improve the state of health in the EU as a whole by implementing standard cohesion policies. To compare efficiency and productivity among the states of the European Union, we used data envelopment analysis (DEA) and the Malmquist productivity index (MPI). On the basis of our findings, even countries that joined the EU later achieve high technical efficiency values. However, it should be noted that it is in these countries that technical efficiency values tend to decline. The values of the Malmquist productivity index broadly indicate stagnation in western countries and productivity decline in central and eastern European countries. This decline is mainly due to a negative shift in the technological frontier in these countries.