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Neurons of the mammalian medullary respiratory center have complex patterns of electrophysiological behavior. Three typical phenomena associated with these patterns are spike frequency adaptation (SFA), delayed excitation (DE), and postinhibitory rebound (PIR). Although several nuclei are associated with the medullary-pontine respiratory center, we focused on neurons from two nuclei: (1) the ventral subnucleus of the nucleus tractus solitarius (vNTS) of the dorsal respiratory group and (2) the nucleus ambiguus (NA) of the ventral respiratory group. We developed a Hodgkin-Huxley (HH) type model of the typical medullary neuron that is capable of mimicking the discharge pattern of real neurons to a very high degree. Closer examination of typical data revealed, however, that there was not one type of medullary respiratory neuron, but at least three (types A, B1, and B2). We classified these neurons based on the electrophysiologic phenomena that they exhibited (type A exhibits DE but not PIR; types B1 and B2 exhibit PIR but not DE; all types are adapting). Our objective was to relate each of these well-known phenomena to specific ionic current mechanisms. In the model, three currents directly affect the phenomena investigated: the Ca2+-activated K+ current, I(K,Ca), controls peak and steady-state firing rates and the time constant of adaptation; the transient outward K+ current, I(A), is responsible for all aspects of DE, including the dependence of delay on the magnitude and duration of conditioning hyperpolarization; and the hyperpolarization-activated current, Ih, elicits PIR and dictates its dependencies. We consider that our HH model represents a unifying structure, whereby different electrophysiological phenomena or discharge patterns can be emulated using different strengths of the component ionic membrane currents (particularly I(K,Ca), I(A), and Ih). Moreover, its predictions suggest that the electrophysiological characteristics of medullary respiratory neurons, from different areas of the brainstem and even from different species, can be modeled using the same structural framework, wherein the specific properties of individual neurons are emulated by adjusting the strengths of key ionic membrane currents in the model.