Internationalism has always been a major strand of anarchist political thought where it works on several levels. It has described their commitment to dynamic cosmopolitanism but also dictated revolutionary strategy and structured their social alternatives. In the post-war years, however, many anarchist thinkers, confronting the implications of the atomic bomb for state power and global governance, acknowledged the need for strategic revision. Retreating from the idea of revolution as a series of national armed uprisings, they shifted, instead, towards endorsing an ‘act local, think global’ approach to policy. But what did it mean to think global? This article focuses on British post-war anarchists and explores their spectrum of approaches to this strategy shift. While it recognises a common move towards more permeable notions of the local-global dynamic, it also argues for a richer differentiation among their responses than is usually acknowledged.