A common element of current theories of speech perception is speech-envelope tracking, the alignment of neural activity to the slow amplitude fluctuations of a speech signal. Cortical speech-envelope tracking has been shown to depend on various acoustic and linguistic speech-signal features as well as cognitive factors. In the present study, we investigate whether cortical speech-envelope tracking depends on the temporal and semantic predictability of the speech input. 23 normally-hearing participants listened to various 30-second passages of continuous natural speech, while their cortical tracking of the speech envelope was measured using scalp electroencephalography (EEG). Predictability was experimentally manipulated by gradually increasing listeners’ familiarity with the speech input over time; i.e., each speech passage was presented five times in direct succession. To disentangle effects of semantic and temporal predictability, a control condition allowing temporal, but not semantic, predictability was included (unintelligible noise-vocoded speech carrying the same envelope as the original speech). Analysis of EEG responses across speech-envelope repetitions reveals higher positive correlations among repetitions of natural speech than repetitions of vocoded speech. Relatively weak correlations are observed between repetitions of the same envelope in natural and vocoded form. These preliminary results suggest that speech intelligibility strongly contributes to the cortical representation of the speech envelope. Ongoing analyses test whether the observed correlation depends on predictability, as operationalised by repetition number. In addition, the repetitions allow analysing the performance (noise) ceiling observable in the current EEG data.