To understand better a possible future constant global population that is demographically heterogeneous, this paper analyzes several models. Classical theory of stationary populations generally fails to apply. However, if constant global population size P(global) is the sum of all country population sizes, and if constant global annual number of births B(global) is the sum of the annual number of births of all countries, and if constant global life expectancy at birth e(global) is the population-weighted mean of the life expectancy at birth of all countries, then B(global) x e(global) always exceeds P(global) unless all countries have the same life expectancy at birth.