The United States and China are the primary nodes of the multinodal world order. Together they are the middle third of the global economy, with the world’s biggest military budgets. Their parity makes rivalry inevitable because they are one another’s greatest counterpart. But their parity is asymmetric. China’s power relies on its demographic scale and on its Pacific Asian integration, while the US remains the center of the familiar global system that it created and it is the avatar of the developed world. While a Cold War is unlikely, the dangers posed by global rivalry are profound, ranging from nuclear war to failure to cooperate on global problems. The primary nodes also face asymmetric challenges. The US faces the challenge of adjusting to a central but not hegemonic global role. China faces the challenge of domestic tolerance and a mutually beneficial integration of Greater China and, more generally, of Pacific Asia. Beyond the primary nodes, regional reduction of uncertainties can contribute to the stabilization of world order. Cooperation founded on mutual respect is the prerequisite of successful global governance in a post-hegemonic world.