International AI governance agreements and institutions may play an important role in reducing global security risks from advanced AI. To inform the design of such agreements and institutions, we conducted case studies of historical and contemporary international security agreements. We focused specifically on those arrangements around dual-use technologies, examining agreements in nuclear security, chemical weapons, biosecurity, and export controls. For each agreement, we examined four key areas: (a) purpose, (b) core powers, (c) governance structure, and (d) instances of non-compliance. From these case studies, we extracted lessons for the design of international AI agreements and governance institutions. We discuss the importance of robust verification methods, strategies for balancing power between nations, mechanisms for adapting to rapid technological change, approaches to managing trade-offs between transparency and security, incentives for participation, and effective enforcement mechanisms.