Higher education has expanded at astonishing rates around the world. We seek to understand the oppositions that periodically arise, which may produce enrollment declines and/or imposition of political controls. The post-1945 growth of higher education was -- to a greater extent than is often recognized -- propelled by the liberal, and later neoliberal, international order. Oppositions arise from illiberal alternatives, which also may organize globally. The recent weakening of the global liberal order, associated with growing populism and nationalism, creates conditions for a new wave of oppositions. We hypothesize that attacks on higher education emerge in countries less integrated into world society and in countries linked to international structures that support illiberal alternatives. We examine cross-national data on higher education over the period 1960-2017. Enrollments and funding are higher in societies more tightly linked to world society and lower in countries tied to illiberal international organizations. Analyses of enrollments in various fields, constraints on academic freedom, and terrorist attacks on education institutions show similar pattern. Finally, we observe heterogeneity in the forms of illiberal opposition: countries that suppress academic freedom generally are less likely to restrict enrollments.