Listening to speech with poor signal quality is challenging. Neural speech tracking of degraded speech has been used to advance the understanding of how brain processes and speech intelligibility are interrelated, however the temporal dynamics of neural speech tracking are not clear. In the present MEG study, we thereby exploited temporal response functions (TRFs) and generated signal-degraded speech to depict the temporal evolution of speech intelligibility modulation on neural speech tracking. In addition, we inter-related facets of neural speech tracking (e.g., speech envelope reconstruction, speech-brain coherence, and components of broadband coherence spectra) to endorse our findings in TRFs. Our TRF analysis yielded marked temporally differential effects of vocoding: reduction of intelligibility went along with large increases of early peak responses (∼50-110 ms, M50TRF), but strongly reduced responses around 175-230 ms (M200TRF). For the late responses 315-380 ms (M350TRF), the maximum response occurred for degraded speech that was still comprehensible then declined with reduced intelligibility. Furthermore, we related the TRF components to our other neural “tracking“ measures and found that M50TRF and M200TRF play a differential role in the shifting center frequency of the broadband coherence spectra. Overall, our study highlights the importance of time-resolved computation and parametrization of coherence spectra on neural speech tracking and provides a better understanding of degraded speech processing.HighlightsWe use MEG to show that speech intelligibility differentially impacts the temporal evolution of neural speech tracking.TRF responses around 200 ms show the strongest relationship with behaviour.Relating TRF effects to parameterized coherence spectra using FOOOF suggests that M50TRF and M200TRF reflect shifts in which speech features are tracked over time.