Little has contributed more to the emergence of today's world of financial globalization than the setup of the international monetary system. In its current shape, it has a hierarchical structure with the US-Dollar (USD) at the top and various other monetary areas forming a multilayered periphery to it. A key feature of the system is the creation of USD offshore – a feature that in the 1950s and 60s developed in co-evolution with the Bretton Woods System and in the 1970s replaced it. Since the 2007–9 Financial Crisis, this ‘Offshore US-Dollar System’ has been backstopped by the Federal Reserve's network of swap lines which are extended to other key central banks. This systemic evolution may continue in the decades to come, but other systemic arrangements are possible as well and have historical precedents. This article discusses four trajectories that would lead to different setups of the international monetary system by 2040, taking into account how its hierarchical structure and the role of offshore credit money creation may evolve. In addition to a continuation of USD hegemony, we present the emergence of competing monetary blocs, the formation of an international monetary federation and the disintegration into an international monetary anarchy.