If the prediction of some scientists comes true, then we are only few years away from the appearance of the first generation of human beings who will be able to add one year to each remaining year of life expectancy. Faced with this possibility, it seems appropriate to give thought to the public policies that should be adopted. It is better to anticipate the various future scenarios than react to a reality which is a fait accompli. To date, the debate has mainly focused on the ethical question: is it good or bad for us humans to achieve immortal life? Until now, neither legal guidelines at State level nor those of international organisations which deal with bioethical issues have concerned themselves with this matter. But before discussing policies, two other matters should be addressed: first, to show how the prolongation of human life can be as much the unwanted outcome of legitimate efforts in search of healthy aging, as one of the aims of the post-humanist project; second, to present the most consistent and shared ethical reasons for rejecting the human immortality project.