This article critically reviews the suggestion that we are experiencing a ‘succession of hegemonies’ from the United States to China. It develops Martin Wight's writings on hegemony, and introduces a fundamental distinction (not made by Wight) between a power transition and a hegemonic succession. Wight held complex views about the nature of power and at times seemed to subscribe to a purely materialist account. Elsewhere he was more nuanced and appealed to the purpose of dominant states as part of his argument that influence does not correlate exactly with mass and weight. This suggestion is developed in the author's view of hegemony—as distinct from primacy—as denoting a legitimate practice within international society. These ideas are then superimposed upon current debates about a power transition, or a succession of hegemonies, as between the United States and China. The existing debate conflates those two issues. Accordingly, while it can readily be acknowledged that there are important indicators of a shift in the material distribution of power, this in no way amounts, as yet, to any kind of hegemonic succession. For the latter to occur, there would need to be clear evidence of an effective socialization of the aspirant hegemon's purpose and support for its preferred order. On the contrary, to date China has been largely content to operate within existing frameworks, rather than instigate a revision of them, and does not yet present a model for emulation elsewhere. It is possible that a power transition, without any hegemonic succession, could be corrosive of global governance.