Based on single-unit recordings of modulation transfer functions (MTFs) in the inferior colliculus (IC) and the medial geniculate body (MGB) of the unanesthetized rabbit, we identified two opposing populations: band-enhanced (BE) and band-suppressed (BS) neurons. In response to amplitude-modulated (AM) sounds, firing rates of BE and BS neurons were enhanced and suppressed, respectively, relative to their responses to an unmodulated noise with a one-octave bandwidth. We also identified a third population, designated hybrid neurons, whose firing rates were enhanced by some modulation frequencies and suppressed by others. Our finding suggests that perception of AM may be based on the co-occurrence of enhancement and suppression of responses of the opposing populations of neurons. Because AM carries an important part of the content of speech, progress in understanding auditory processing of AM sounds should lead to progress in understanding speech perception. Each of the BE, BS, and hybrid types of MTFs comprised approximately one-third of the total sample. Modulation envelopes having short duty cycles of 20-50% and raised-sine envelopes accentuated the degree of enhancement and suppression and sharpened tuning of the MTFs. With sinusoidal envelopes, peak modulation frequencies were centered around 32-64 Hz among IC BE neurons, whereas the MGB peak frequencies skewed toward lower frequencies, with a median of 16 Hz. We also tested an auditory-brainstem model and found that a simple circuit containing fast excitatory synapses and slow inhibitory synapses was able to reproduce salient features of the BE- and BS-type MTFs of IC neurons. Opposing populations of neurons have been identified in the mammalian auditory midbrain and thalamus. In response to amplitude-modulated sounds, responses of one population (band-enhanced) increased whereas responses of another (band-suppressed) decreased relative to their responses to an unmodulated sound. These opposing auditory populations are analogous to the ON and OFF populations of the visual system and may improve transfer of information carried by the temporal envelopes of complex sounds such as speech.