Everyday conversation requires listeners to quickly recognize verbal actions, so-called speech acts, from the underspecified linguistic code and prepare a relevant response within the tight time constraints of turn-taking. The goal of this study was to determine the time-course of speech act recognition by investigating oscillatory EEG activity during comprehension of spoken dialogue. Participants listened to short, spoken dialogues with target utterances that delivered three distinct speech acts (Answers, Declinations, Pre-offers). The targets were identical across conditions at lexico-syntactic and phonetic/prosodic levels but differed in the pragmatic interpretation of the speech act performed. Speech act comprehension was associated with reduced power in the alpha/beta bands just prior to Declination speech acts, relative to Answers and Pre-offers. In addition, we observed reduced power in the theta band during the beginning of Declinations, relative to Answers. Based on the role of alpha and beta desynchronization in anticipatory processes, the results are taken to indicate that anticipation plays a role in speech act recognition. Anticipation of speech acts could be critical for efficient turn-taking, allowing interactants to quickly recognize speech acts and respond within the tight time frame characteristic of conversation. The results show that anticipatory processes can be triggered by the characteristics of the interaction, including the speech act type.