(A) Stimuli consisted of 8 continuous 6 min long audio-visual speech samples. For each condition we extracted the acoustic speech envelope as well as the temporal trajectory of the lip contour (video frames, top right: magnification of lip opening and contour). (B) The experimental design comprised eight conditions, defined by the factorial combination of 4 levels of speech to background signal to noise ratio (SNR = 2, 4, 6, and 8 dB) and two levels of visual informativeness (VI: Visual context Informative: video showing the narrator in synch with speech; VN: Visual context Not informative: video showing the narrator producing babble speech). Experimental conditions lasted 1 (SNR) or 3 (VIVN) minutes, and were presented in pseudo-randomized order. (C) Analyses were carried out on band-pass filtered speech envelope and MEG signals. The MEG data were source-projected onto a grey-matter grid. One analysis quantified speech entrainment, i.e. the mutual information (MI) between the MEG data and the acoustic speech envelope (speech MI), as well as between the MEG and the lip contour (lip MI), and the extent to which these were modulated by the experimental conditions. A second analysis quantified directed functional connectivity (DI) between seeds and the extent to which this was modulated by the experimental conditions. A final analysis assessed the correlation of either MI or DI with word-recognition performance. Relevant variables in deposited data (doi:10.5061/dryad.j4567): SE_speech; LE_lip.