This study examines the demographic perspectives of Wallony, the French language region of Belgium. It identifies the problem of zero growth of the population when compared to world trends and seeks to evaluate a policy of stationary evolution. The analysis concludes with a comparison of Wallony and Québec. Initially, the author examines the exponential growth of world population and involves the notions of Malthus and the more recent concepts of the « Limits to Growth » movement. He then looks at the evolution of he population of Wallony since the înde- pendance of Belgium until the most recent census year, 1970. The relative decline of the Wallon population is highlighted. Accepting as false the alternatives of a stoppage or slowing of growth at the planetary scale or a take-off at the level of Wallony, the author qualifies the « stationary solution » as utopie. At the scale of Wallony, the article analyses the evolution of the demographic structure and identifies characteristics of a policy based upon a moderate increase of birth rates and upon the integration of foreign elements residing within the population. The study draws a parallel with the situation in Québec, emphasizing that the two populations resemble each other with respect to natural processes but differ with respect to demographic structure.