This study investigates the importance of the phase relation between vagal activity and the resulting chronotropic effect on the heart’s pacemaker. Both the transient nature of the pacemaker response to a single vagal burst of activity, preceded and followed by silence, and the steady-state pacemaker response to a continuous periodic vagal activity are examined. The response to transient vagal activity has two salient characteristics; 1) vagal activity which occurs sufficiently late in a pacemaker period will have no effect on that period; however, the following periods will be altered. 2) the first period in which the stimulus occurs will be either increased or remain unchanged (as stated in 1); the second and third periods may be decreased below the control period, depending upon the phase relation between vagal and pacemaker activity and the intensity of the vagal activity; the fourth, fifth, and etc. periods are greater than the control period and decay exponentially to the control period as the time from stimulus increases. This information is presented in the form of the Inhibition Curve. The pacemaker response to vagal activity becomes locked (entrained) to the steady-state vagal activity at the fundamental, ie, one occurrence of vagal activity during each pacemaker period, and at higher and subharmonics of the vagal activity rate. This entrainment phenomena was evident in the constant phase relation between the pacemaker and vagal activity. During entrainment an increase in the rate of vagal activity would cause a paradoxical increase in the pacemaker rate; however, over the entire spectrum of vagal activity rate, the trend was the expected decrease in pacemaker rate with increased vagal activity rate. A mathematical model has been developed to mimic pacemaker response to vagal activity. The model is composed of a relaxation oscillator with an unforced rate corresponding to the denervated pacemaker rate. The neuro-chemical transmitter and its effect on the pacemaker is modeled with a linear filter and nonlinear gain. The vagal stimulus is represented by an impulse in the model. Data has been obtained from the dog where vagal activity was initiated by supramaximal burst stimulation of the vagus nerve (1 msec pulses with 11 msec intraburst period) of 1,3 or 5 pulses/burst. Propranolol was administered (1 mg/kg) to block all sympathetic activity, and atrial activity, via a bipolar electrode in the atrium, was used as an indication of the pacemaker activation. The model parameters were chosen such that the model responded to transient activation as did the data. The model was then shown to exhibit entrainment to continuous periodic input as does the data.