This paper describes low-frequency auditory steady-state responses (ASSRs) to speech-weighted noise stimuli. The effect of modulation frequency was evaluated within the frequency range below 40 Hz. Furthermore, objective ASSR measures were related to speech understanding performance in normal-hearing and hearing-impaired listeners. The variability in ASSR recordings over independent test sessions was larger between subjects than within. Trends of increased responses around 10 and/or 20 Hz were found in all subjects. Obtained latency estimates of the responses pointed to primarily cortical sources involved in ASSR generation at low frequencies. Furthermore, significant differences between normal-hearing and hearing-impaired adults were found for ASSRs to stimuli related to the temporal envelope of speech. Comparing these responses with phoneme identification scores over different stimulus levels showed both measures increased with stimulus level in a similar way (rho=0.82). At a fixed stimulus level, ASSRs were significantly correlated with speech reception thresholds for phonemes and sentences in noise (rho from -0.45 to -0.53). These results indicate that objective low-frequency ASSRs are related to behavioral speech understanding, independently of level.