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In the European communities, the need for tax harmonization has begun to commence since the beginning of integration efforts in the 1960s. The first attitudes to tax harmonization were very ambitious. The plan was not only structural harmonization but also harmonization of tax rates. The paper examines the nature and course of the direct tax harmonization process, describes its advantages and disadvantages as well as the positive and negative effects of tax competition. The paper aims to examine the development and volume of selected income taxes collected in the Member States of the European Union. It tells whether the harmonization of income taxes is still a stagnant process. Cluster analysis deals with looking for similarities of multidimensional objects. Two clustering methods were used – hierarchical agglomeration clustering and non-hierarchical clustering. Cluster analysis aimed to achieve groups of states that would have some homogeneity. Cluster analysis sorted the data into sets with the highest possible similarity within the group and the most significant difference between the groups. Analysis of tax burden and income tax rates confirmed significant differences in these indicators across the EU. On the other hand, cluster analysis revealed similar developments in tax systems in terms of their geographical location in Europe. Cluster analysis can be used to suggest possible steps to co-operate in harmonizing Member State taxes in the future. The authors of this article propose the possibility of harmonizing taxes and cooperating gradually within clusters rather than trying to apply uniform rules in all EU Member States at the same time. The conclusion of the article raises problems in the field of harmonization of direct taxes in the EU. The possibility of preserving autonomy in deciding on tax burden in the country is left to the many Member States because they see that autonomy as a competitive advantage, particularly in the field of investment. [ABSTRACT FROM AUTHOR]