It was reported earlier that an inhibitory-feedback network inspired by neostriatal circuitry may exhibit a bistable character and spontaneous switching phenomenon within the neuronal activity. In the presence of noise and external excitation, a few local neurons switch "on" and generate streams of impulses while other neurons remain quiescent. In time, the existing "on" neurons spontaneously switch "off" and other neurons switch "on". In this paper we examine the nature of the bistability and switching phenomenon using a simple model consisting of two mutually inhibitory neurons. For nonspiking neuron model, described by a system of nonlinear differential equations, we present a simple bifurcation analysis, which follows the birth and annihilation of two stable fixed points when model parameters are varied. We show that both nonspiking and spiking models may have two stable states, but only spiking neurons exhibit switching. The mechanism of switching for model spiking neurons, described by an equivalent RC circuit with a number of currents, is analyzed using computer simulations. It is shown that switching can be described by a two-state Markov chain with one parameter, which depends on the set of model physiological parameters, such as duration of afterhyperpolarization (AHP), maximum and the time duration of inhibitory post-synaptic potentials (IPSP's) and amplitude of the neuron noise input. "On" and "off" states of the model can be rapidly changed by localized excitatory input and the network then sustains the pattern of "on" and "off" states. That is, such a network can be used as a programmable memory device.(ABSTRACT TRUNCATED AT 250 WORDS)