There is a close relationship among the types of sleep apnea (central, obstructive, and mixed) in regard to both the pathogenesis and in the clinical management of sleep apnea syndromes. This review will recount the rationale for the use of animal models in understanding intermediate traits, such as the ventilatory responses to hypoxia and reoxygenation, seen with human sleep apnea. One feature of particular interest will be the dynamic responses of the control system, specifically the instability over time that could operate to produce repetitive apneas. The recurrent nature of clinically significant sleep apnea can be understood in terms of feedback control, or “loop gain”. We will discuss findings in a mouse model for recurrent apneas and propose that there exist genetic mechanisms that could determine loop gain in the respiratory control system.