Qualified personnel plays an important role in the competition between countries for economic leadership that enables the transition to a multipolar world. In this context, the higher education sphere is changing; universities worldwide are increasingly striving to attract the best students to their country. The study aims to identify factors causing changes in the position of universities in world regions and develop recommendations for Russian universities to strengthen their positions in the global education market. The methodology relies on the concept of different historical cycles leading to changes in world leaders. The article offers a contemporary interpretation of higher education internationalisation as a multidimensional process instead of fragmentation. The first section explores the issue of changing the world leader; the second identifies transformations in higher education internationalisation in key world regions; the third assesses university internationalisation as a basis for new rankings and self-assessment. A hypothesis about the correlation between the trend of changing global leaders and the place of national universities in international rankings is confirmed. To assess the trend dynamics, the article proposes authors' multidimensional indices of higher education and university internationalisation for world countries. It is revealed that China, aspiring to be a world leader, has expanded its share in the education market and increased import volumes by more than 1.5 times, sending its students to high-ranking universities, while the USA has weakened its position. Russian universities occupy middle positions in rankings despite the growth of the country's share in the global education market. Recommendations offered to Russian universities and the option of their self-assessment can be used by strategic development professionals. © 2024 Institute of Economics, Ural Branch of the Russian Academy of Sciences. All rights reserved.