Recent studies on the bat's auditory system indicate that the corticofugal system mediates a highly focused positive feedback to physiologically "matched" subcortical neurons, and widespread lateral inhibition to physiologically "unmatched" subcortical neurons, to adjust and improve information processing. These findings have solved the controversy in physiological data, accumulated since 1962, of corticofugal effects on subcortical auditory neurons: inhibitory, excitatory, or both (an inhibitory effect is much more frequent than an excitatory effect). In the mustached bat, Pteronotus parnellii parnellii, the inferior colliculus, medial geniculate body, and auditory cortex each have "FM-FM" neurons, which are "combination-sensitive" and are tuned to specific time delays (echo delays) of echo FM components from the FM components of an emitted biosonar pulse. FM-FM neurons are more complex in response properties than cortical neurons which primarily respond to single tones. In the present study, we found that inactivation of the entire FM-FM area in the cortex, including neurons both physiologically matched and unmatched with subcortical FM-FM neurons, on the average reduced the facilitative responses to paired FM sounds by 82% for thalamic FM-FM neurons and by 66% for collicular FM-FM neurons. The corticofugal influence on the facilitative responses of subcortical combination-sensitive neurons is much larger than that on the excitatory responses of subcortical neurons primarily responding to single tones. Therefore we propose the hypothesis that, in general, the processing of complex sounds by combination-sensitive neurons more heavily depends on the corticofugal system than that by single-tone sensitive neurons.