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The world-system is in a structural crisis. This is not merely a downturn in some parameters, but a moment when the system has moved too far from equilibrium and bifurcated. Two scenarios are possible, which are the object of a political debate: which scenario will ultimately prevail as a result of an infinity of nano-actions by an infinity of actors at an infinity of nano-moments. The outcome cannot be predicted, but it is certain that one of the two scenarios will eventually prevail. The paper traces how a capitalist world-economy normally functions and how the processes enabling the maximum accumulation of capital degenerate over time, leading to a structural crisis. It traces the mode of functioning of the two principal cyclical rhythms of the historical system - the Kondratieff curves and the hegemonic curves - and why they have now come close to asymptotes. It also traces the impact of the1968 world-revolution on the capacity of the system to sustain its geoculture, and the return to independent operation of both the conservative right and the radical left, now liberated from the constraints of the liberal center.