Abstract. The paper is based upon a review of three new books devoted to the big emerging countries in Latin America and Asia. One of these books was written by the Russian scholar Lev Klochkovskii. The authorship of two other books belongs to Pierre Salama, a well-known French specialist in developing countries. The starting point for consideration of the mentioned works is the fact of convergence between the North and the South. This convergence involves quantitative economic indicators as well as qualitative aspects of development: the rise of innovations and R&D centres, enterprises outputting high-tech goods, etc. All these and some other trends require revision of old concepts of “centre” and “periphery” in the world system. However, the countries under consideration have entered the period of slowdown, and risk to fall into a middle income trap. It means that their development models have been exhausting and need to be profoundly changed. In the case of Latin American countries, the difficulties arisen recently are aggravated by the impact of China. The manufacturing industries in Brazil and Mexico loose competiveness under pressure of goods imported from China. It brings about a relative de-industrialisation of Latin American economies. At the same time, the recent development in China becomes increasingly resembling to the Brazilian situation of the 1970s when the economic growth was mostly advantageous for the upper, upper middle and, partly, middle classes. It led to the deepening of social differentiation and, thereby, restrained the internal market. This trend can be interpreted as  “Latin Americanisation” of China. Can the big emerging countries change trajectories of their development? If not, they will appear as the colossi with feet of clay rather than the real centres of economic power.