We developed a mathematical model of "respiratory" sinus arrhythmia. The model combines a representation continuous in time of the parasympathetic and sympathetic innervation and the membrane potential of the pace maker cell of the heart with a beat-by-beat representation of the cardiovascular variables like diastolic and systolic blood pressure, pulse pressure, total peripheral resistance and baroreceptor activity. The influence of respiration is described separately by mechanical and central neural mechanisms. Using this nonlinear model of "respiratory" heart rate variability one is able to explore in a theoretical way the different heart rate variability generating mechanisms, either as isolated or combined effects on both, heart rate variability in the frequency range of respiration and in the frequency range around 0.1 Hz. By fitting a simulated RR interval time course to a physiological RR interval time course one can estimate the relative weight of the different mechanisms generating this physiological heart rate variability.