Humans can understand spoken or written sentences presented at extremely fast rates of ∼400 wpm, far exceeding the normal speech rate (∼150 wpm). How does the brain cope with speeded language? And what processing bottlenecks eventually make language incomprehensible above a certain presentation rate? We used time-resolved fMRI to probe the brain responses to spoken and written sentences presented at five compression rates, ranging from intelligible (60–100% of the natural duration) to challenging (40%) and unintelligible (20%). The results show that cortical areas differ sharply in their activation speed and amplitude. In modality-specific sensory areas, activation varies linearly with stimulus duration. However, a large modality-independent left-hemispheric language network, including the inferior frontal gyrus (pars orbitalis and triangularis) and the superior temporal sulcus, shows a remarkably time-invariant response, followed by a sudden collapse for unintelligible stimuli. Finally, linear and nonlinear responses, reflecting a greater effort as compression increases, are seen at various prefrontal and parietal sites. We show that these profiles fit with a simple model according to which the higher stages of language processing operate at a fixed speed and thus impose a temporal bottleneck on sentence comprehension. At presentation rates faster than this internal processing speed, incoming words must be buffered, and intelligibility vanishes when buffer storage and retrieval operations are saturated. Based on their temporal and amplitude profiles, buffer regions can be identified with the left inferior frontal/anterior insula, precentral cortex, and mesial frontal cortex.