The autonomous global system of science, grounded in collegial networks of scientists, publishing, and cross-border papers, is expanding rapidly and spreading to a growing number of countries. Strong national science systems have emerged outside Euro-America. Yet the multipolarization of economic capacity and scientific output plays out within a continuing Euro-American science world regulated by an inside/outside binary. Global science remains primarily Anglo-American in language, leading institutions, disciplinary and publishing regimes, agendas, and topics. Non-English and endogenous knowledges are excluded. The article critiques the world-systems theory interpretation of relations of power in science. The determinist center-periphery model fails to grasp the growth and pluralization of global science and its relation with national science systems. It normalizes the Eurocentrism it opposes, radically underestimating agency outside the "center" countries. The article argues for a more ontologically open theorization of global power in science, in terms of cultural hegemony, and for an ecology-of-knowledges approach.