International criminal law (ICL) is an achievement, but at the same time a challenge to the traditional conception of the principle of legality (_lex praevia_, _scripta_, and _stricta_ – Sect. 1). International criminal tribunals have often based conviction for international crimes on unwritten norms the existence and scope of which they have failed to substantiate. In so doing, they have evaded the objection that they were applying _ex post facto_ criminal laws. This approach, the relaxation of the concept of law (...) by including norms whose existence is doubtful, has apparently served to maintain a concept of strict legality, but it is unsatisfying (Sect. 2). In my opinion, the strict principle of legality that has linked its absolute validity to the positivity of law is not the correct premise. It makes sense to state that positivity and validity do not necessarily go hand in hand (Sect. 3). Applied to ICL, this means that it is neither necessary nor convincing to “conceal” supra-positive law as positive law, as some decisions of the international criminal tribunals do. For this reason, I consider that Radbruch’s formula, consisting in admitting that there are supra-positive limits which positive law must respect in order to be valid, is well-founded (Sect. 4). The path taken by this significant philosopher of law is methodologically convincing, and it squarely faces the problem of the value of positive law. Nevertheless, if we admit Radbruch’s formula and thereby the limited value of positive law (if we claim that the validity of the law depends on it respecting supra-positive minimums of justice), we must also face the problem of the definition of supra-positive values, the epistemological difficulties of having access to them (Sect. 5), and the question of the scope and enforceability of supra-positive law (Sect. 6). In summary, this article aims to explain why Radbruch’s formula offers a convincing conceptual basis for international criminal legality and, in doing so, aims to contribute to the discussion about the foundations of ICL. (shrink)