Article dans une revue: While Lotka and Lopez proposed conditions on (exogenous) fertility and mortality laws under which populations with distinct initial age structures exhibit the same asymptotic age structure, this paper re-examines age-structure stabilization and convergence by considering a three-period overlapping generations model where fertility and longevity are determined by human capital accumulation and by intergenerational trade. It is shown that the age structure must converge asymptotically towards a stable structure, and that populations with distinct initial age structures end up with the same long-run age structure when fertility and mortality laws are converging, which requires converging intergenerational terms of trade.