Metabolic production of CO2 varies according to task (exercise, speaking, etc.). The human body maintains homeostasis (i.e., a constant CO2 content in blood), by varying alveolar ventilation, V˙A. The regulatory mechanism involves the breathing apparatus (lungs, airways, diaphragm), affecting V˙A, and the medullary pontine respiratory center (MPRC) in the brain stem. The MPRC is responsible for generating the basic rhythm of breathing and corrects for disturbances. Neurons inside the MPRC are organized into a central pattern generator (CPG), the functionality of which is not clearly understood. Although intracellular recordings have established the stimulus-induced response of isolated respiratory neurons in specific locales of the brain stem, the emerging properties of the CPG have not been directly correlated with intrinsic neuronal behavior. We develop computer-based models that emulate the regulatory operation of respiration. We adopt a systems view of the process, whereby the breathing apparatus (mechanics model) represents the plant, actuated by the respiratory muscles and controlled by the CPG. The mechanics model has two degrees of freedom (for lung and airway motion) and exhibits hysteresis and other nonlinearities. A frequency domain analysis of a linearized model is used to estimate parameters. The mechanics model is validated against data (lung volume and intrapleural pressure) collected from volunteer human subjects in a pulmonary function lab. The CPG is modeled as a neuronal network. We develop and validate a Hodgkin-Huxley type neuronal model that can mimic, with biophysical realism, the response of isolated neurons in the ventral Nucleus Tractus Solitarius and Nucleus Ambiguus of experimental animals. Characteristic nonlinearities of neuronal behavior, such as spike frequency adaptation, delayed excitation and postinhibitory rebound are captured successfully. The proposed network generates a stable, realistic breathing rhythm and responds successfully to disturbances. Moreover, individual firing patterns of experimentally identified respiratory neurons (early-I, ramp-I, late-I, post-I, E2 and pre-I) mimic data closely. Computer simulations show that adaptation in the firing rate of specific neurons dictates the duration of respiratory phases (inspiration, post-inspiration and expiration) and provides a mechanism for phase switching.