Recent psychophysics data suggest that speech perception is not limited by the capacity of the auditory system to encode fast acoustic variations through neural γ activity, but rather by the time given to the brain to decode them. Whether the decoding process is bounded by the capacity of θ rhythm to follow syllabic rhythms in speech, or constrained by a more endogenous top-down mechanism, e.g., involving β activity, is unknown. We addressed the dynamics of auditory decoding in speech comprehension by challenging syllable tracking and speech decoding using comprehensible and incomprehensible time-compressed auditory sentences. We recorded EEGs in human participants and found that neural activity in both θ and γ ranges was sensitive to syllabic rate. Phase patterns of slow neural activity consistently followed the syllabic rate (4-14 Hz), even when this rate went beyond the classical θ range (4-8 Hz). The power of θ activity increased linearly with syllabic rate but showed no sensitivity to comprehension. Conversely, the power of β (14-21 Hz) activity was insensitive to the syllabic rate, yet reflected comprehension on a single-trial basis. We found different long-range dynamics for θ and β activity, with β activity building up in time while more contextual information becomes available. This is consistent with the roles of θ and β activity in stimulus-driven versus endogenous mechanisms. These data show that speech comprehension is constrained by concurrent stimulus-driven θ and low-γ activity, and by endogenous β activity, but not primarily by the capacity of θ activity to track the syllabic rhythm.SIGNIFICANCE STATEMENT Speech comprehension partly depends on the ability of the auditory cortex to track syllable boundaries with θ-range neural oscillations. The reason comprehension drops when speech is accelerated could hence be because θ oscillations can no longer follow the syllabic rate. Here, we presented subjects with comprehensible and incomprehensible accelerated speech, and show that neural phase patterns in the θ band consistently reflect the syllabic rate, even when speech becomes too fast to be intelligible. The drop in comprehension, however, is signaled by a significant decrease in the power of low-β oscillations (14-21 Hz). These data suggest that speech comprehension is not limited by the capacity of θ oscillations to adapt to syllabic rate, but by an endogenous decoding process.