What explains the rising tensions in trade politics between the U.S. and China? Unlike existing research, which points to the domestic distributional effects of trade with China, we highlight the international political concerns that arise from the transition of power between the two countries. We expect that public support for bilateral economic cooperation shrinks in the declining country because citizens are increasingly concerned about unequal gains from international economic cooperation. In contrast, citizens in the rising country are keen to foster global cooperation in order to credibly signal that they will not behave aggressively in the future. By means of a survey experiment with nationally representative samples from both China and the United States, we examine how citizens respond to information about the evolution of their countries' economic power vis-à-vis one another. The results confirm our hypotheses. Moreover, the impact of the power transition on support for bilateral cooperation is similar across partisan camps and among citizens with diverse socio-economic status.