If there is a set of issues where great power cooperation could be most likely, it should be in the global commons. Global commons issues are-by definition-shared by multiple nations. As part of a broader study of great power cooperation in an era of strategic competition, the authors assessed the potential for U.S. cooperation with China or Russia on eight global commons issues: maintaining freedom of access to space, dismantling transnational criminal organizations/networks, countering violent extremist organizations, promoting global stability, preserving access to the air and maritime commons, preventing nuclear arms races, preventing militarization of the Arctic, and maintaining the openness of cyberspace. The authors sought to understand where the United States, China, and Russia share interests on these issues, what the obstacles to cooperation are, and where the United States might be able to deepen its cooperation with one or both powers. The authors find that the trade space for cooperation is already narrow and usually focused more on civilian aspects of these domains rather than core security matters. In general, there is more room for the United States to cooperate with Russia than with China, and there are significant obstacles to cooperation, with a lack of trust being the most common. Finally, cooperation produces both positive and negative externalities, and the costs of cooperation do not always outweigh the likely benefits.