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We present and test a hypothesis which, to the best of our knowledge, is new in the demographic field: the age structure of any population in any period tends towards a specific shape, which can be identified in advance. This “attractor†is the age structure of the current stationary population, which we label RAS, or “reference age structureâ€. There is no mathematical demonstration for this tendency: however, we show that it exists in practice, measure the speed of the convergence (of the current on the reference age structure), and discuss the theoretical and practical utility of the notion.