Behavioral research demonstrates a critical transition in preschooler's mental-state understanding (i.e., theory of mind; ToM), revealed most starkly in performance on tasks about a character's false belief (e.g., about an object's location). Questions remain regarding the neural and cognitive processes differentiating children who pass versus fail behavioral false-belief tasks and the extent to which there is continuity versus change in the ToM neural network. To address these questions, we analyzed event-related spectral power in the electroencephalogram (EEG) to investigate how preschoolers' neural activity during passive viewing of false-belief scenarios related to their explicit behavioral ToM performance. We found that neural activity during passive viewing of false-belief events (6-9Hz EEG 'alpha' suppression in right temporoparietal [RTP] electrodes) strongly related to children's explicit ToM. However, children's RTP alpha suppression differed depending on their explicit behavioral ToM performance: Children who did better on a broad battery of standard ToM tasks and who passed explicit behavioral false-belief tasks showed greater RTP alpha suppression when the character's belief first became false (during the 'location-change' event); whereas children who did worse on the ToM battery and who failed explicit behavioral false-belief tasks showed greater RTP alpha suppression only later when they could evaluate the character's behavior in the context of prior events (during the 'active-search' event). Findings shed light on what differentiates preschoolers who pass versus fail explicit false-belief tasks and raise questions about how to interpret existing neuroscience data from ToM tasks across infancy to adulthood. RESEARCH HIGHLIGHTS: Preschool children's neural activity (EEG 6-9Hz suppression in right temporoparietal [RTP] electrodes) during passive-viewing of false-belief events was related to their explicit behavioral theory-of-mind performance. Children who did better on a theory-of-mind (ToM) battery and passed explicit false-belief tasks showed greater RTP alpha suppression when the character's belief first became false. Children who performed worse on the ToM battery and failed explicit false-belief tasks showed greater RTP alpha suppression later when observing the character's search behavior. Findings reveal change in preschoolers' ToM neural correlates and suggest that the presence of RTP activity does not necessarily indicate 'mature' theory of mind.