Certain invertebrate neurons generate endogenous bursts of action potentials due to an underlying slow membrane potential oscillation. An early hypothesis for the oscillations proposed a high resting sodium conductance that led to the depolarizing phase, followed by activation of an electrogenic sodium pump coupled to chloride ions, leading to the hyperpolarizing phase. Recent findings contradict this hypothesis. Current thought implicates two conductances in the generation of the oscillations. The depolarizing phase is due to an increase in a sodium or a calcium conductance; the hyperpolarizing phase is due to a subsequent increase in a potassium conductance, which may be either voltage dependent or triggered by an influx of calcium ions. The observation of a negative slope conductance region in the membrane I-V characteristic supports this hypothesis. Bursting cells also usually exhibit anomalous rectification, i.e., a decrease in slope conductance with depolarization, in the I-V characteristic. This decrease may result from a decrease in an outward current or an increase in an inward current. The more important bursting membrane characteristics have been incorporated into an electronic analog. The analog confirms the appropriateness of the two-conductance hypothesis. It also suggests that potassium ion accumulation outside the cell membrane may enhance bursting activity.