Quantitative structure-activity relationships (QSAR) models have been used for decades to predict the activity of small molecules, using encodings of the molecular structure, for which simple 2D descriptors of the molecular graph are still most commonly used. One of the recurrent problems of QSAR is that relationships observed for a specific scaffold (pruned molecular skeleton) are often not transferable to another; this is often addressed by building several local models from subsets of the chemical space. Similarly, single task models sometimes outperform large multi-task models in predicting the activity of small molecules against specific proteins. In this paper, we introduce Glolloc, a global-local MoE-QSAR architecture, based on a Mixture of Experts (MoE) framework. Glolloc combines predictions from global and local experts, provides a built-in model introspection tool, can enhance model performance, and removes the need to maintain several local models.