Speech contains complex amplitude modulations that have envelopes with multiple temporal cues. The processing of these complex envelopes is not well explained by the classical models of amplitude modulation processing. This may be because the evidence for the models typically comes from the use of simple sinusoidal amplitude modulations. In this study we used magnetoencephalography (MEG) to generate source space current estimates of the steady-state responses to simple one-component amplitude modulations and to a two-component amplitude modulation. A two-component modulation introduces the simplest form of modulation complexity into the waveform; the summation of the two-modulation rates introduces a beat-like modulation at the difference frequency between the two modulation rates. We compared the cortical representations of responses to the one-component and two-component modulations. In particular, we show that the temporal complexity in the two-component amplitude modulation stimuli was preserved at the cortical level. The method of stimulus normalization that we used also allows us to interpret these results as evidence that the important feature in sound modulations is the relative depth of one modulation rate with respect to another, rather than the absolute carrier-to-sideband modulation depth. More generally, this may be interpreted as evidence that modulation detection accurately preserves a representation of the modulation envelope. This is an important observation with respect to models of modulation processing, as it suggests that models may need a dynamic processing step to effectively model non-stationary stimuli. We suggest that the classic modulation filterbank model needs to be modified to take these findings into account.