Brain oscillations are prevalent in all species and are involved in numerous perceptual operations. α oscillations are thought to facilitate processing through the inhibition of task-irrelevant networks, while β oscillations are linked to the putative reactivation of content representations. Can the proposed functional role of α and β oscillations be generalized from low-level operations to higher-level cognitive processes? Here we address this question focusing on naturalistic spoken language comprehension. Twenty-two (18 female) Dutch native speakers listened to stories in Dutch and French while MEG was recorded. We used dependency parsing to identify three dependency states at each word: the number of (1) newly opened dependencies, (2) dependencies that remained open, and (3) resolved dependencies. We then constructed forward models to predict α and β power from the dependency features. Results showed that dependency features predict α and β power in language-related regions beyond low-level linguistic features. Left temporal, fundamental language regions are involved in language comprehension in α, while frontal and parietal, higher-order language regions, and motor regions are involved in β. Critically, α- and β-band dynamics seem to subserve language comprehension tapping into syntactic structure building and semantic composition by providing low-level mechanistic operations for inhibition and reactivation processes. Because of the temporal similarity of the α-β responses, their potential functional dissociation remains to be elucidated. Overall, this study sheds light on the role of α and β oscillations during naturalistic spoken language comprehension, providing evidence for the generalizability of these dynamics from perceptual to complex linguistic processes.