Sixteen patients with confirmed obstructive sleep apnea syndrome (OSAS) each participated in 2 overnight sleep studies: one before and one after 3 months of home treatment with continuous positive airway pressure (CPAP). The patients were divided into "compliant" and "non-complaint" groups, based on average nightly CPAP use. Respiration, R-R interval (RRI), blood pressure and other polysomnographic variables were recorded during wakefulness, stage 2 and rapid eye-movement sleep. Using a Volterra-Wiener model and the Laguerre expansion technique, we estimated the parameters that characterize the linear and second-order nonlinear effects of respiration ("RSA") and arterial blood pressure ("ABR") on heart rate. Mean RRI as well as linear and nonlinear ABR gains increased in the compliant OSAS patients. The opposite was observed in the non-compliant group. Our results suggest that long-term CPAP therapy can lead to significant improvement of cardiac autonomic function, but the degree of change depends strongly on the level of compliance. Left untreated, OSAS can lead to continual degradation of autonomic control. The nonlinear modeling approach represents a novel noninvasive means of monitoring autonomic function in OSAS patients as they undergo therapy by CPAP or other modalities.