Abstract: The ‘Thucydides trap’ exaggerates the risk of war breaking out between the rising power and the ruling power in the contemporary age. The greater challenge facing China and the United States is to avoid falling into the ‘Churchill trap’. That is, falling into a long-term confrontation by repeating the mistakes of the Cold War between the US and the USSR. Both the ‘old’ history of the ancient East Asian bipolar system and the current experience of Sino-US interaction in East Asia suggest that, in addition to hegemonic war and cold war, there is a third type of great power relationship between the two poles, which I call ‘co-ruling’, whereby rather than being geographically demarcated according to their respective ‘spheres of influence’, the two superpowers jointly lead all or most of the small and medium-sized countries in the system. The theoretical and case studies examined in the article imply that the ‘co-ruling’ mode will appear and be sustained at a time when the two superpowers’ foreign functions are differentiated (i.e. each of the two poles can only meet one of the indispensable needs of small countries, and the two needs that the two poles can respectively meet are different ones), when inter-great-power war is no longer a viable strategic option. The antagonistic and geopolitical colours of the Cold War ‘divided-ruling’ mode of power politics will be less strident in the ‘co-ruling’ mode, so offering an illuminating escape from both the ‘Thucydides trap’ and the ‘Churchill trap’. Full text available here.