Traditionally, demographers, statisticians and political experts have believed that there are three age groups in the population: the young (less than 20 years of age), the adults and the elderly (from the age of 60 onwards). This classification is clear and convenient but irrelevant. We have always known that there are at least three groups as far as the young are concerned: babies, children and adolescents. It is time to recognize that there are two groups in what is disparagingly referred to as the "third age": the "young-old" (60-74 years of age), almost all in good health, active and independent, and the "old-old" (75 years of age and over), who suffer from a progressive deterioration in their health and quality of life. The method of demographic projection allows one to predict, in a very precise manner, the way the numbers in these two age groups will change until the middle of this century. To do this, we need to turn to the results published in 1994 by INSEE for the population of metropolitan France, in the context of plausible hypotheses about the change in mortality and migratory balance. According to these calculations, the French population should reach a ceiling at around 65 million people, the "over 60 years of age" group increasing from a fifth to a third of the population; in particular, in this group, the number of "old-old" will catch up with then, and finally overtake, the number of "young-old": in 2050, unless there is a sudden change, one Frenchman out of six will be over 75 years of age. This internal reversal of the top part of the pyramid cannot fail to have major economic, social and political repercussions, particularly as far as the healthcare budget is concerned.