The global politics of nuclear disarmament has become deeply contested over the past decade, particularly around the negotiation of the 2017 Treaty on the Prohibition of Nuclear Weapons (TPNW). Different explanations are offered, but these tend to centre on the geopolitics of the ‘security environment’ conceived in realist terms. This article makes sense of the TPNW and the global politics of nuclear disarmament by examining its underlying discourse and contestation within a wider framework of nuclear hegemony and resistances to it, drawing on Robert Cox’s theory of hegemony. It argues that the politics of nuclear disarmament has hardened into a contestation between two broadly incommensurable nuclear worldviews, or nuclear ontologies: hegemonic nuclearism and subaltern anti-nuclearism. These are not just different perspectives, but fundamentally different ways of understanding global nuclear politics that have important implications for the nuclear disarmament movement. Three conclusions emerge from this: that intersectionality is vital to understanding subaltern anti-nuclearism within wider processes of resistance in global politics; that contestation between hegemonic nuclearism and subaltern anti-nuclearism is agonistic; and that ‘bridge building’ approaches to find a middle ground generally deny this agonism and thereby close down debate, and that this explains why they often fail to gain traction. The article builds on the critical scholarship on nuclear hegemony, discourse and resistance and develops an original framework of hegemonic and subaltern nuclearism and anti-nuclearism.