Most models of neural networks have assumed that neurons process information on a timescale of milliseconds and that the long-term modification of synaptic strengths underlies learning and memory. But neurons also have cellular mechanisms that operate on a timescale of tens or hundreds of milliseconds, such as a gradual rise in firing rate in response to injection of constant current or a rapid rise followed by a slower adaptation. These dynamic properties of neuronal responses are mediated by ion channels that are subject to modulation. We demonstrate here how a neural network with recurrent feedback connections can convert long-term modulation of neural responses that occur over these intermediate timescales into changes in the amplitude of the steady output from the system. This general principle may be relevant to many feedback systems in the brain. Here it is applied to the vestibulo-ocular reflex, whose amplitude is subject to long-term adaptive modification by visual inputs. The model reconciles apparently contradictory data on the neural locus of the cellular mechanisms that mediate this simple form of learning and memory.