Why do increases in globalisation in the face of European expansion lead to sharp levels of regional divergences in wealth in some countries but not in others? The central crux of this paper is that convergence/divergence trends in European states are conditioned by ‘state capacity’. State capacity –which we define here as a combination of impartial bureaucratic practices, corruption and the rule of law – limits, and in some cases reverses the tendency towards greater divergence linked to trade. Countries with high levels of state capacity – that is, those that have greater government effectiveness, stronger rule of law and lower corruption – experience lower levels of divergence, as they have the mechanisms to counterbalance the strong centripetal forces linked to openness. This claim is tested on countries that have experienced relatively high levels of increases in levels of economic and political globalisation – European Union (EU) member states – using aggregated regional-level data from 1995 to 2008. Strong and robust empirical evidence is found for this claim.