Societal Impact StatementSurveillance of plant pathogens is usually designed according to country boundaries. Benefits of a global surveillance system to tackle long‐distance dispersed crop pathogens are unquantified. Here, a ‘non‐cooperative’ and a ‘cooperative’ strategy are compared in terms of minimizing the surveillance effort to achieve given domestic and global targets. Although a ‘cooperative’ strategy is always more suitable, impacts of its adoption are not equally distributed among countries. Medium‐sized countries in central Europe and Asia would benefit the most from reducing the domestic effort, whereas others would need to deploy more sentinels than they would place in their own interests.Summary Transboundary diseases are extremely complex to control and can cause global socio‐economic damage. In the context of crop protection, surveillance strategies are usually designed according to country boundaries, regardless of the spatial scale of the spread of the disease. In this study, we investigate the suitability of this scale for surveilling long‐distance dispersed pathogens. We use an epidemic network describing worldwide potential transport of Puccinia graminis, the causal agent of stem rust of wheat, modelled in a previous work. Based on network properties, we conceive two strategies for prioritizing areas to be monitored for the presence of the disease, either cooperative or each country alone, and we compare their performances in terms of minimizing the effort deployed in achieving given surveillance targets at global and domestic level. We find that a cooperative strategy is more efficient at the global scale. However, its adoption implies a heterogeneous geographic distribution of surveillance effort‐related costs and benefits. Medium‐sized countries in central Europe and Asia would benefit the most; on the other hand, countries placed in important spreading pathways should deploy more surveillance effort than they would place without cooperation. Among the major wheat producers, China is the only country that may have a cost from a cooperative strategy, whereas India, Russia, the United States, France and Ukraine would have the most benefits. The acknowledgement of how costs and benefits of a global governance would be shared among countries is needed to gain unanimous support for an international cooperative surveillance system.