Auditory steady-state responses (ASSR) to amplitude modulated (AM) tones with carrier frequencies between 250 and 4000 Hz and modulation frequencies near 40 Hz were recorded using a 37-channel neuro-magnetometer placed above the auditory cortex contralateral to the stimulated right ear. The ASSR sources were likely in the primary auditory cortex, located more anteriorly and more medially than the N1m sources. The ASSR amplitude decreased with increasing carrier frequency, the amplitude at 250 Hz being three times larger than at 4000 Hz. The amplitude of the ASSR to a test sound decreased in the presence of an interfering second AM sound. This suppression of the ASSR to the test stimulus was greater when the carrier frequency of the interfering stimulus was higher than that of the test tone and was greater when the test stimulus had a lower carrier frequency. Similar frequency specificity was observed when the interfering sound was a non-modulated pure tone. These results differ from those found for the ASSR elicited by modulation frequencies above 80 Hz or for the transient brainstem and middle-latency responses and suggest substantial interactions between phase-locked activities at the level of the primary auditory cortex.