We investigated computer models of a single thalamocortical neuron to assess the interaction of intrinsic voltage-sensitive channels and cortical synaptic input in producing the range of oscillation frequencies observed in these cells in vivo. A morphologically detailed model with Hodgkin-Huxley-like ion channels demonstrated that intrinsic properties would be sufficient to readily produce 3 to 6 Hz oscillations. Hyperpolarization of the model cell reduced its oscillation frequency monotonically whether through current injection or modulation of a potassium conductance, simulating the response to a neuromodulatory input. We performed detailed analysis of highly reduced models to determine the mechanism of this frequency control. The interburst interval was controlled by two different mechanisms depending on whether or not the pacemaker current, IH, was present. In the absence of IH, depolarization during the interburst interval occurred at the same rate with different current injections. The voltage difference from the nadir to threshold for the low-threshold calcium current, IT, determined the interburst interval. In contrast, with IH present, the rate of depolarization depended on injected current. With the full model, simulated repetitive cortical synaptic input entrained oscillations up to approximately double the natural frequency. Cortical input readily produced phase resetting as well. Our findings suggest that neither ascending brainstem control altering underlying hyperpolarization, nor descending drive by repetitive cortical inputs, would alone be sufficient to produce the range of oscillation frequencies seen in thalamocortical neurons. Instead, intrinsic neuronal mechanisms would dominate for generating the delta range (0.5-4 Hz) oscillations seen during slow wave sleep, whereas synaptic interactions with cortex and the thalamic reticular nucleus would be required for faster oscillations in the frequency range of spindling (7-14 Hz).