This study has as its object the administrative discretion in the light of the premises of neo-constitutionalism. It distinguishes the legalist theory, in which the source of discretion is the legislation, from the neo-constitutionalist theory, in which the source is the Law, globally considered. It dissociates legislative reference from discretion. It examines the subject in the light of the formal principles’ theory. It studies the various aspects of the subject, including the difference between legislative and administrative discretion, technical discretion, the lack of jurisdictional discretion, administrative restrictions on discretion, the vices inherent to discretion, the control of discretion and discretionary extinction.