To what extent do rules of general international law apply between international organizations and their members? The article tackles this question by distinguishing between two categories of relations: those that take place on the international plane and those that are, rather, situated on the institutional plane constituted by the organization’s internal law. I argue that general international law applies by default to relations belonging to the first category, only being displaced when the internal law of an organization contains applicable lex specialis, but that it cannot claim a similar role at the level of internal institutional relations. The question there becomes one concerning the dialogue between relatively autonomous international legal orders, so that it is the internal law of each organization that defines the terms on which rules of international law are allowed in. At the same time, a normative argument can be made for a ‘monistic presumption’ for the application of general international law in cases where the rules of the organization are silent. By delving into such questions of applicable law and identifying the relevant analytical frameworks, the article aims to help international lawyers dealing with complex disputes opposing international organizations and their members to structure the legal analysis.