Electroencephalographic hyperscanning was used to investigate interbrain synchronization patterns in dyads of participants interacting through speech. Results show that brain oscillations are synchronized between listener and speaker during oral narratives. This interpersonal synchronization is mediated in part by a lower-level sensory mechanism of speech-to-brain synchronization, but also by the interactive process that takes place in the situation per se. These results demonstrate the existence of brain-to-brain entrainment which is not merely an epiphenomenon of auditory processing, during listening to one speaker. The study highlights the validity of the two-person neuroscience framework for understanding induced brain activity, and suggests that verbal information exchange cannot be fully understood by examining the listener's or speaker's brain activity in isolation.