Phase-locked responses are vital for auditory perception and they may vary with participants’ arousal state and age. Two phase-locked neural responses that reflect fine-grained acoustic properties of speech were examined in the current study: the frequency-following response (FFR) to the speech fundamental frequency (F0), which originates primarily from the auditory brainstem, and the theta-band phase-locked response (θ-PLV) to the speech envelope that originates from the auditory cortices. The ways these responses were affected by arousal in adults across a wide age-range (19–75 years) were examined. Extracts from electroencephalographic (EEG) responses to repeated syllables were classified into either high or low arousal state based on the occurrence of sleep spindles. The magnitudes of both FFRs and θ-PLVs were statistically greater in the high, than in the low, arousal state. The difference in θ-PLV between the two arousal states was significantly associated with sleep spindle density in the young, but not the older, adults. The results show that (1) arousal affects phase-locked processing of speech at cortical/sub-cortical sensory levels; and that (2) there is an interplay between aging and arousal state which indicates that sleep spindles have an age-dependent neuro-regulatory role on cortical processes. The results lay the grounds for studying how cognitive states affect early-stage neural activity in the auditory system across the lifespan.