The relationship between the evoked responses (ERPs/ERFs) and the event‐related changes in EEG/MEG power that can be observed during sentence‐level language comprehension is as yet unclear. This study addresses a possible relationship between MEG power changes and the N400m component of the event‐related field. Whole‐head MEG was recorded while subjects listened to spoken sentences with incongruent (IC) or congruent (C) sentence endings. A clear N400m was observed over the left hemisphere, and was larger for the IC sentences than for the C sentences. A time–frequency analysis of power revealed a decrease in alpha and beta power over the left hemisphere in roughly the same time range as the N400m for the IC relative to the C condition. A linear regression analysis revealed a positive linear relationship between N400m and beta power for the IC condition, not for the C condition. No such linear relation was found between N400m and alpha power for either condition. The sources of the beta decrease were estimated in the LIFG, a region known to be involved in semantic unification operations. One source of the N400m was estimated in the left superior temporal region, which has been related to lexical retrieval. We interpret our data within a framework in which beta oscillations are inversely related to the engagement of task‐relevant brain networks. The source reconstructions of the beta power suppression and the N400m effect support the notion of a dynamic communication between the LIFG and the left superior temporal region during language comprehension.