The pre-Bötzinger complex is a small region in the mammalian brainstem involved in generation of the respiratory rhythm. As shown in vitro, this region, under certain conditions, can generate endogenous rhythmic bursting activity. Our investigation focused on the conditions that may induce this bursting behaviour. A computational model of a population of pacemaker neurons in the pre-Bötzinger complex was developed and analysed. Each neuron was modelled in the Hodgkin–Huxley style and included persistent sodium and delayed-rectifier potassium currents. We found that the firing behaviour of the model strongly depended on the expression of these currents. Specifically, bursting in the model could be induced by a suppression of delayed-rectifier potassium current (either directly or via an increase in extracellular potassium concentration, [K+]o) or by an augmentation of persistent sodium current. To test our modelling predictions, we recorded endogenous population activity of the pre-Bötzinger complex and activity of the hypoglossal (XII) nerve from in vitro transverse brainstem slices (700 µm) of neonatal rats (P0–P4). Rhythmic activity was absent at 3 mm[K+]o but could be triggered by either the elevation of [K+]o to 5–7 mm or application of potassium current blockers (4-AP, 50–200 µm, or TEA, 2 or 4 mm), or by blocking aerobic metabolism with NaCN (2 mm). This rhythmic activity could be abolished by the persistent sodium current blocker riluzole (25 or 50 µm). These findings are discussed in the context of the role of endogenous bursting activity in the respiratory rhythm generation in vivo vs. in vitro and during normal breathing in vivo vs. gasping.