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Event-centric structured prediction involves predicting structured outputs of events. In most NLP cases, event structures are complex with manifold dependency, and it is challenging to effectively represent these complicated structured events. To address these issues, we propose Structured Prediction with Energy-based Event-Centric Hyperspheres (SPEECH). SPEECH models complex dependency among event structured components with energy-based modeling, and represents event classes with simple but effective hyperspheres. Experiments on two unified-annotated event datasets indicate that SPEECH is predominant in event detection and event-relation extraction tasks.