Cochlear damage can change the spontaneous firing rates of neurons in the dorsal cochlear nucleus (DCN). Increased spontaneous firing rates (hyperactivity) after acoustic trauma have been observed in the DCN of rodents such as hamsters, chinchillas and rats. This hyperactivity has been interpreted as a neural correlate of tinnitus. In cats, however, the spontaneous firing rates of DCN neurons were not significantly elevated after acoustic trauma. Species-specific spontaneous firing rates after cochlear damage might be attributable to differences in the response types of DCN neurons: In gerbils, type III response characteristics are predominant, whereas in cats type IV responses are more frequent. To address the question of how the development of hyperactivity after cochlear damage depends on the response type of DCN neurons, we use a computational model of the basic circuit of the DCN. By changing the strength of two types of inhibition, we can reproduce salient features of the responses of DCN neurons. Simulated cochlear damage, which decreases the activity of auditory nerve fibers, is assumed to activate homeostatic plasticity in projection neurons (PNs) of the DCN. We find that the resulting spontaneous firing rates depend on the response type of DCN PNs: PNs with type III and type IV-T response characteristics may become hyperactive, whereas type IV PNs do not develop increased spontaneous firing rates after acoustic trauma. This theoretical framework for the mechanisms and circumstances of the development of hyperactivity in central auditory neurons might also provide new insights into the development of tinnitus.