We study the relationship of injected current to oscillator period in single neurons and two-cell model networks formed by reciprocal inhibitory synapses. Using a Morris-Lecar-like model, we identify two qualitative types of oscillatory behavior for single model neurons. The "classical" oscillator behavior is defined as type A. Here the burst duration is relatively constant and the frequency increases with depolarization. For oscillator type B, the frequency first increases and then decreases when depolarized, due to the variable burst duration. Our simulations show that relatively modest changes in the maximal inward and outward conductances can move the oscillator from one type to another. Cultured stomatogastric ganglion neurons exhibit both A and B type behaviors and can switch between the two types with pharmacological manipulation. Our simulations indicate that the stability of a two-cell network with injected current can be extended with inhibitory coupling. In addition, two-cell networks formed from type A or type B oscillators behave differently from each other at lower synaptic strengths.