The biomedicalization process and the rise of genetics that have occurred in the last few decades raise political issues concerning the ability of subjects in biomedicine to act and make choices. My work examines these issues through a study of the process by which neonatal screening for the genetic disease of cystic fibrosis (CF) was set up in France. It draws on qualitative interviews with 25 national officials making use of the Foucauldian notion of government, which implies power relations among entities recognized as subjects of action. I examine how different agents (or groups) came to form either governing or governable entities within this health policy, and by what means governance in this area is exercised. The study positions relations between governors and the governed in the dynamics specific to them, showing that screening for CF is, to a large degree, a political technique for governing self and others based on a biomedical technique. Two types of subject (a professionals' association and a patients' association) are seen to be constituted in different ways and endowed with more or less extensive power. More generally, the study raises the question of the form of the political, through the example of genetic screening.