Pre-print, Working paper: While demographers Lotka (1939) and Lopez (1961) 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 the issues of age structure stabilization and convergence, by considering a population whose fertility and mortality are endogenously determined in the economy. For that purpose, we develop a three-period OLG model where human capital accumulation and intergenerational trade affect fertility and longevity. It is shown that the age structure must converge asymptotically towards a stable structure, whose form depends on the structural parameters of the economy. Moreover, populations with distinct initial age structures will end up with the same long-run age structure when fertility and mortality laws are converging, which requires converging terms of trade between coexisting generations in the different populations under study.