EEG studies employing time–frequency analysis have revealed changes in theta and alpha power in a variety of language and memory tasks. Semantic and syntactic violations embedded in sentences evoke well-known ERPs, but little is known about the oscillatory responses to these violations. We investigated oscillatory responses to both kinds of violations, while monolingual and bilingual participants performed an acceptability judgment task. Both violations elicited power decreases (event-related desynchronization, ERD) in the 8–30 Hz frequency range, but with different scalp topographies. In addition, semantic anomalies elicited power increases (event-related synchronization, ERS) in the 1–5 Hz frequency band. The 1–5 Hz ERS was strongly phase-locked to stimulus onset and highly correlated with time domain averages, whereas the 8–30 Hz ERD response varied independently of these. In addition, the results showed that language expertise modulated 8–30 Hz ERD for syntactic violations as a function of the executive demands of the task. When the executive function demands were increased using a grammaticality judgment task, bilinguals but not monolinguals demonstrated reduced 8–30 Hz ERD for syntactic violations. These findings suggest a putative role of the 8–30 Hz ERD response as a marker of linguistic processing that likely represents a separate neural process from those underlying ERPs.