Technology diffusion contributes to the technological and economic convergence of countries. The rapid spread of Internet technologies creates bases to put forward a hypothesis about the convergence of countries in terms of their level of penetration. The purpose of the study is to identify a trend towards convergence or divergence in both fixed and mobile broadband for the countries of the world as a whole and for groups of countries identified on the basis of the following criteria: geographical (by geographic macro-regions), economic (by national income per capita), and institutional (according to membership in an international organization). The data sources were the open data of the International Telecommunication Union. The research methodology includes the construction of dynamic models on panel data to test the hypothesis of the presence of unconditional beta convergence. In addition, the absolute scale of the digital divide between groups of countries in terms of broadband Internet access was estimated using a sigma convergence model. The results of the study indicate the presence of beta convergence for both fixed and mobile broadband. This pattern is observed both for the full sample of countries and for geographic regions, with the exception of Oceania. Also, beta convergence is typical for groups of countries identified by the level of income per capita and participation in the Organization for Economic Cooperation and Development. At the same time, the results of the study indicate a persistent digital divide between countries in terms of Internet broadband penetration. The practical significance includes recommendations developed on the basis of the research findings, aimed at implementing a strategy for accelerated technological development in order to stimulate the spread of mobile broadband access and expand the telecommunications infrastructure.