When do relations between a rising state and a hegemonic state deteriorate? Scholarship in international relations theory maintains that when the rising state meets the three criteria of the power transition theory baseline – higher growth rates, power parity, and frustration with the status quo – relations between it and the hegemonic state deteriorate. These conditions alone cannot explain the timing and shape of the rising state to challenge the hegemonic state. In this article we introduce scope and boundary conditions for power transition theory, focusing on the rising state’s challenge and its effects on power transition dynamics. We propose that a rising state’s challenge to the hegemonic state is contingent on two variables: only when the rising state translates its gross power rise into advanced military capabilities and perceives the hegemonic state to have low resolve will it escalate its strategy against the hegemonic state and deteriorate their relations. An examination of three case studies – US–China relations (1991–2024), Spain–Portugal relations (1469–94), and Germany–UK relations (1871–1914) – support this argument.