The paper deals with the impact of centre-periphery relations on the demographic change in Europe in the 21st century. The reasons why the projections presented by Statistics Netherlands and the Netherlands Interdisciplinary Demographic Institute in 1999 underestimated the future population growth in France, Italy, Spain and UK are analyzed. Current statistics and UN population projections (2012 revision) demonstrate that the idea of the total depopulation coming in Europe, commonly held there over the 20th century, is out of date. In fact, depopulation is far from being total; it is common only in peripheral countries of Europe, not in semi-peripheral and central ones (Germany is an exception). This conclusion is corroborated by the close positive correlation (r=0.754) between per capita GNI and the rate of population increase in 34 European countries between 2000 and 2012. The alarmist perspective of ageing is criticized. It is argued that ageing is often unreasonably blamed for negative effects which, in fact, are caused by other faults of socioeconomic system. So, the recent number of unemployed in Spain (5.7 millions) is four times more than the expected decrease in the number of people aged 20 to 64 between 2010 and 2030 (1.4 millions). The prospective institutional and structural consequences of the post-crisis shifting of immigration flows from Spain to Germany are considered. Given this shifting, the further expansion of the peripheral and semi-peripheral enclaves in German economy seems to be verisimilar. Nevertheless, the centripetal migration maintains, like before, the centre-peripheral differences in Europe. The centre concentrates knowledge-intensive services and attracts the most qualified migrants; semi-periphery receives the less qualified ones; the periphery is the source of labour force for both the centre and the semi-periphery.