The amplitude envelope of speech carries crucial low-frequency acoustic information that assists linguistic decoding at multiple time scales. Neurophysiological signals are known to track the amplitude envelope of adult-directed speech (ADS), particularly in the theta-band. Acoustic analysis of infant-directed speech (IDS) has revealed significantly greater modulation energy than ADS in an amplitude-modulation (AM) band centered on ~2 Hz. Accordingly, cortical tracking of IDS by delta-band neural signals may be key to language acquisition. Speech also contains acoustic information within its higher-frequency bands (beta, gamma). Adult EEG and MEG studies reveal an oscillatory hierarchy, whereby low-frequency (delta, theta) neural phase dynamics temporally organize the amplitude of high-frequency signals (phase amplitude coupling, PAC). Whilst consensus is growing around the role of PAC in the matured adult brain, its role in the development of speech processing is unexplored. Here, we examined the presence and maturation of low-frequency (<12 Hz) cortical speech tracking in infants by recording EEG longitudinally from 60 participants when aged 4-, 7- and 11- months as they listened to nursery rhymes. After establishing stimulus-related neural signals in delta and theta, cortical tracking at each age was assessed in the delta, theta and alpha [control] bands using a multivariate temporal response function (mTRF) method. Delta-beta, delta-gamma, theta-beta and theta-gamma phase-amplitude coupling (PAC) was also assessed. Significant delta and theta but not alpha tracking was found. Significant PAC was present at all ages, with both delta and theta -driven coupling observed.