Propofol-mediated unconsciousness elicits strong alpha/low-beta and slow oscillations in the electroencephalogram (EEG) of patients. As anesthetic dose increases, the EEG signal changes in ways that give clues to the level of unconsciousness; the network mechanisms of these changes are only partially understood. Here, we construct a biophysical thalamocortical network involving brainstem influences that reproduces transitions in dynamics seen in the EEG involving the evolution of the power and frequency of alpha/low beta and slow rhythm, as well as their interactions.Our model suggests propofol engages thalamic spindle and cortical sleep mechanisms to elicit persistent alpha/low-beta and slow rhythms, respectively. The thalamocortical network fluctuates between two mutually exclusive states on the timescale of seconds. One state is characterized by continuous alpha/low-beta frequency spiking in thalamus (C-state), while in the other, thalamic alpha spiking is interrupted by periods of co-occurring thalamic and cortical silence (I-state). In the I-state, alpha co-localizes to the peak of the slow oscillation; in the C-state, there is a variable relationship between an alpha/beta rhythm and the slow oscillation. The C-state predominates near loss of consciousness; with increasing dose, the proportion of time spent in the I-state increases, recapitulating EEG phenomenology. Cortical synchrony drives the switch to the I-state by changing the nature of the thalamocortical feedback. Brainstem influence on the strength of thalamocortical feedback mediates the amount of cortical synchrony. Our model implicates loss of low-beta, cortical synchrony, and coordinated thalamocortical silent periods as contributing to the unconscious state.