Preventing major events, like the India blackout in 2012 or the Fukushima nuclear disaster in 2011, is vital for the safety of society. Automated diagnosis may play an important role in this prevention. However, a gap still exists between the complexity of systems such these and the effectiveness of state-of-the-art diagnosis techniques. The contribution of this paper is twofold: the definition of a novel class of discrete-event systems (DESs), called higherorder DESs (HDESs), and the formalization of a relevant diagnosis technique. HDESs are structured hierarchically in several cohabiting subsystems, accommodated at different abstraction levels, each one living its own life, as happens in living beings. The communication between subsystems at different levels relies on complex events, occurring when specific patterns of transitions are matched. Diagnosis of HDESs is scalable, context-sensitive, and in a way intelligent.