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Both in vivo and in vitro recordings indicate that neuronal membrane potentials can make spontaneous transitions between distinct up and down states. At the network level, populations of neurons have been observed to make these transitions synchronously. Although synaptic activity and intrinsic neuron properties play an important role, the precise nature of the processes responsible for these phenomena is not known. Using a computational model we explore the interplay between intrinsic neuronal properties and synaptic fluctuations. Model neurons of the integrate-and-fire type were extended by adding a nonlinear membrane current. Networks of these neurons exhibit large amplitude synchronous spontaneous fluctuations that make the neurons jump between up and down states, thereby producing bimodal membrane potential distributions. The effect of sensory stimulation on network responses depends on whether the stimulus is applied during an up state or deeply inside a down state. External noise can be varied to modulate the network continuously between two extreme regimes in which it remains permanently in either the up or the down state.