During linguistic processing, a set of brain regions on the lateral surfaces of the left frontal, temporal, and parietal cortices exhibit robust responses. These areas display highly correlated activity while a subject rests or performs a naturalistic language comprehension task, suggesting that they form an integrated functional system. Evidence suggests that this system is spatially and functionally distinct from other systems that support high-level cognition in humans. Yet, how different regions within this system might be recruited dynamically during task performance is not well understood. Here we use network methods, applied to fMRI data collected from 22 human subjects performing a language comprehension task, to reveal the dynamic nature of the language system. We observe the presence of a stable core of brain regions, predominantly located in the left hemisphere, that consistently coactivate with one another. We also observe the presence of a more flexible periphery of brain regions, predominantly located in the right hemisphere, that coactivate with different regions at different times. However, the language functional ROIs in the angular gyrus and the anterior temporal lobe were notable exceptions to this trend. By highlighting the temporal dimension of language processing, these results suggest a trade-off between a region's specialization and its capacity for flexible network reconfiguration.