During their early years, infants use the temporal statistics of the speech signal to boot-strap language learning, but the neural mechanisms that facilitate this temporal analysis are poorly understood. In adults, neural oscillatory entrainment to the speech amplitude envelope has been proposed to be a mechanism for multi-time resolution analysis of adult-directed speech, with a focus on Theta (syllable) and low Gamma (phoneme) rates. However, it is not known whether developing infants perform multi-time oscillatory analysis of infant-directed speech with the same temporal focus. Here, we examined infants' processing of the temporal structure of sung nursery rhymes, and compared their neural entrainment across multiple timescales with that of well-matched adults (their mothers). Typical infants and their mothers (N=58, median age 8.3 months) viewed videos of sung nursery rhymes while their neural activity at C3 and C4 was concurrently monitored using dual-electroencephalography (dual-EEG). The accuracy of infants' and adults' neural oscillatory entrainment to speech was compared by calculating their phase-locking values (PLVs) across the EEG-speech frequency spectrum. Infants showed better phase-locking than adults at Theta (~4.5 Hz) and Alpha (~9.3 Hz) rates, corresponding to rhyme and phoneme patterns in our stimuli. Infant entrainment levels matched adults' for syllables and prosodic stress patterns (Delta,~1-2 Hz). By contrast, infants were less accurate than adults at tracking slow (~0.5 Hz) phrasal patterns. Therefore, compared to adults, language-learning infants' temporal parsing of the speech signal shows highest relative acuity at Theta-Alpha rates. This temporal focus could support the accurate encoding of syllable and rhyme patterns during infants' sensitive period for phonetic and phonotactic learning. Therefore, oscillatory entrainment could be one neural mechanism that supports early bootstrapping of language learning from infant-directed speech (such as nursery rhymes).