Slow acoustic modulations below 20 Hz, of varying bandwidths, are dominant components of speech and many other natural sounds. The dynamic neural representations of these modulations are difficult to study through noninvasive neural-recording methods, however, because of the omnipresent background of slow neural oscillations throughout the brain. We recorded the auditory steady-state responses (aSSR) to slow amplitude modulations (AM) from 14 human subjects using magnetoencephalography. The responses to five AM rates (1.5, 3.5, 7.5, 15.5, and 31.5 Hz) and four types of carrier (pure tone and 1/3-, 2-, and 5-octave pink noise) were investigated. The phase-locked aSSR was detected reliably in all conditions. The response power generally decreases with increasing modulation rate, and the response latency is between 100 and 150 ms for all but the highest rates. Response properties depend only weakly on the bandwidth. Analysis of the complex-valued aSSR magnetic fields in the Fourier domain reveals several neural sources with different response phases. These neural sources of the aSSR, when approximated by a single equivalent current dipole (ECD), are distinct from and medial to the ECD location of the N1m response. These results demonstrate that the globally synchronized activity in the human auditory cortex is phase locked to slow temporal modulations below 30 Hz, and the neural sensitivity decreases with an increasing AM rate, with relative insensitivity to bandwidth.