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The object of the study is the competitiveness of the economies of the Eurasian Economic Union (EAEU) countries. Assessment of the level of competitiveness is one of the urgent problems of the modern economy. There are still no uniform methods and standards in the world for defining the concept of «competitiveness of the economy», methods for its assessment and factors influencing it, which raises many questions regarding the comparison of the level of development and competitiveness of world economies. Given the comparative advantages of economies, different methodological approaches may produce different results in relation to the competitive position of a given country. In the course of the study, the author presented the developed mathematical model for calculating the competitiveness of the similarity and dissimilarity index, which comprehensively characterizes the state of the economy of the Eurasian Economic Union countries. Thus, comparing the measure of similarity or dissimilarity of countries according to different methods will undoubtedly give a comprehensive idea of their competitiveness, as well as allow the development of an appropriate and effective economic policy. The analysis in the paper of the dynamics of the index of similarity and dissimilarity in the external economic activities of Kazakhstan with the EAEU countries over the years, it is possible to establish the trend observed in this process, and, consequently, to determine the strategy of international economic relations for the future. The results of the study can be used by government agencies that make decisions in the field of trade, economic and investment cooperation. [ABSTRACT FROM AUTHOR]