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A mathematical model of neonatal respiratory control which can be used to simulate the system under different physiological conditions is proposed. The model consists of a continuous plant and a discrete controller. Included in the plant are lungs, body tissue, brain tissue, a cerebrospinal fluid compartment, and central and peripheral receptors. The effect of shunt in the lungs is included in the model, and the lung volume and the dead space are time varying. The controller utilizes outputs from peripheral and central receptors to adjust the depth and rate of breathing, and the effects of prematurity of peripheral receptors are included in the system. Hering-Breuer-type reflexes are embodied in the controller to accomplish respiratory synchronization. The model is examined and its simulation results under test conditions in hypoxia and hypercapnia are presented.