This article draws on Niklas Luhmann's theory and method to present transnational social movement organizations as a solution to the problem of increased expectations of global public goods which fail to find adequate accommodation in law. As a concrete example of the limits of law in this respect, it examines the non liquet of the World Court on the question of the illegality of nuclear weapons. The trajectory of anti‐nuclear norms is traced beyond the limits of law to the alternative structure of transnational social movement organizations, and the article presents such organizations as stabilizing increased expectations of global public goods through their recursive decision making and their capacity to continuously project those expectations at the legal and political systems. This generates observations on the concept of ‘global governance ‘, the structural relations between global civil society and international law, and the role of this form of organization in the evolution of the global political system.