Brain activity is known to track the amplitude envelope of adult-directed speech (ADS). Infant-directed speech (IDS) has significantly greater modulation energy than ADS in an amplitude-modulation (AM) band centered on ~2 Hz. Accordingly, cortical tracking of speech by delta-band neural signals may be critical for language acquisition. We examined the presence and maturation of low frequency (<12Hz) cortical speech tracking, recording EEG longitudinally from 60 infants aged 4-, 7-, and 11- months listening to sung nursery rhymes. After establishing stimulus-induced 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, the earliest such demonstration for speech. Significant PAC was present at all ages, with stronger delta-driven coupling observed, as hypothesised.