Slow oscillatory activity (<1 Hz) is observed in vivo in the cortex during slow-wave sleep or under anesthesia and in vitro when the bath solution is chosen to more closely mimic cerebrospinal fluid. Here we present a biophysical network model for the slow oscillations observed in vitro that reproduces the single neuron behaviors and collective network firing patterns in control as well as under pharmacological manipulations. The membrane potential of a neuron oscillates slowly (at <1 Hz) between a down state and an up state; the up state is maintained by strong recurrent excitation balanced by inhibition, and the transition to the down state is due to a slow adaptation current (Na(+)-dependent K(+) current). Consistent with in vivo data, the input resistance of a model neuron, on average, is the largest at the end of the down state and the smallest during the initial phase of the up state. An activity wave is initiated by spontaneous spike discharges in a minority of neurons, and propagates across the network at a speed of 3-8 mm/s in control and 20-50 mm/s with inhibition block. Our work suggests that long-range excitatory patchy connections contribute significantly to this wave propagation. Finally, we show with this model that various known physiological effects of neuromodulation can switch the network to tonic firing, thus simulating a transition to the waking state.