Using a Volterra-Wiener model and the Laguerre expansion technique, we estimated in a previous study the parameters that characterize linear and the second order effects of respiration ("RSA") and arterial blood pressure ("ABR") on heart rate. RSA and ABR gains were significantly lower in Obstructive Sleep Apnea (OSA) patients than in normal subjects. During sleep, ABR gain increased in normals but remained unchanged in OSA. In the present work, we investigated the physiological interpretation of the nonlinear components of the described model of heart rate variability, by means of simulation on the computed linear and nonlinear kernels. Our results indicate that the 2nd order kernels reflect specific characteristics of the RSA and ABR mechanisms, such as a RSA freq uency response dependence upon tidal volume, saturation in the ABR-Blood Pressure relation, and respiratory modulation of ABR. © 2005 IEEE.