What constitutes 'law' in the efflorescent field of 'global administrative law'? This article argues for a 'social fact' conception of law, emphasizing sources and recognition criteria, but it extends this Hartian positivism to incorporate requirements of 'publicness' in law. 'Publicness' is immanent in public law in national democratic jurisprudence, and increasingly in global governance, where it applies to public entities rather than to identifiable global publics. Principles relevant to publicness include the entity's adherence to legality, rationality, proportionality, rule of law, and some human rights. This article traces growing use of publicness criteria in practices of judicial-type review of the acts of global governance entities, in requirements of reason-giving, and in practices concerning publicity and transparency. Adherence to requirements of publicness becomes greater, the less the entity is able to rely on firmly established sources of law and legal recognition. 'Private ordering' comes within this concept of law only through engagement with public institutions. While there is no single unifying rule of recognition covering all of GAL, there is a workable concept of law in GAL.