RTs in conversation, with average gaps of 200 msec and often less, beat standard RTs, despite the complexity of response and the lag in speech production (600 msec or more). This can only be achieved by anticipation of timing and content of turns in conversation, about which little is known. Using EEG and an experimental task with conversational stimuli, we show that estimation of turn durations are based on anticipating the way the turn would be completed. We found a neuronal correlate of turn-end anticipation localized in ACC and inferior parietal lobule, namely a beta-frequency desynchronization as early as 1250 msec, before the end of the turn. We suggest that anticipation of the other's utterance leads to accurately timed transitions in everyday conversations.