This article focuses on the phenomenon of global rivalry between China and the United States in terms of power transition theory, which is scientifically new and relevant due to the increased attention to the so-called Thucydides trap, in which, as some experts claim, both states have fallen. This paper presents a different vision of the global rivalry for leadership in the shaping of a new world order, which has already taken the form of overt non-violent confrontation and manifests itself in technological and trade wars as well as scientific and cultural rivalries. Nevertheless, despite the non-violent nature of the rivalry, this process is followed by an increase in the military capabilities of states, mainly projected in the basins of the Pacific and Indian Oceans (Indo-Pacific region). The methodological basis of the paper is power transition theory, which has been developed over the past 60 years by A.F. Organsky, J. Kugler, D. Lemke, R. Tammen and other researchers, united in the TransResearch Consortium. The authors argue that the analytical prism of this theory is more relevant to the analysis of current global rivalry than the classical neorealist balance of power approach. Through the prism of the theory the issues of rebalancing the global system of economic governance are analyzed. Also, a comparative analysis of the US-Japanese and US-Chinese trade and technological wars is carried out. Both the military and aggregate capabilities of two countries on a global scale and in the Indo-Pacific region are examined. The conclusion contains findings and comments on the impact of U.S. - China rivalry on the system of international relations.