Spoken language and music are characterized by hierarchical structures that unfold over time. Listening to speech and music, therefore, requires the brain not only to process syllables or notes, but also to internally construct high-level linguistic and musical structures (e.g., words and phrases; beats and motifs) and anticipate incoming contents. In this talk, I will present two studies on ancient Chinese poetry and Western classical music, in which we probed mechanisms of hierarchical structure building and prediction in speech and music perception. Using MEG and EEG recording, we discovered low-frequency neural oscillatory components (< 1Hz) that reliably parsed musical and linguistic high-level structures. We next identified a phenomenon – phase precession, suggesting that listeners established structural predictions for high-level structural boundaries. The data reveal candidate brain mechanisms that listeners use to segment continuous music and speech streams and to predict abstract structural linguistic and musical features.