Infants master temporal patterns of their native language at a developmental trajectory from slow to fast:Shortly after birth, they recognize the slow acoustic modulations specific to their native language before tuning into faster language-specific patterns between 6-12 months of age. We here propose that this trajectory is constrained by neuronal maturation-in particular, the gradual emergence of high-frequency neural oscillations in the infant electroencephalogram. Infants' initial focus on slow prosodic modulations is consistent with the prenatal availability of slow electrophysiological activity (i.e., theta-- and delta-band oscillations). Our proposal is consistent with the temporal patterns of infant-directed speech, which initially amplifies slow modulations, approaching the faster modulation range of adult-directed speech only as infants' language has advanced sufficiently. Moreover, our proposal agrees with evidence from premature infants showing maturational age is a stronger predictor of language development than ex-utero exposure to speech, indicating that premature infants cannot exploit their earlier availability of speech because of electrophysiological constraints.In sum, we provide a new perspective on language acquisition emphasizing neuronal development as critical driving force of infants' language development.