A new model of smooth pursuit eye movements is presented. We begin by formally analyzing the stability of the proportional-derivative (PD) model of smooth pursuit eye movements using Pontryagin's theory. The PD model is the linearized version of the nonlinear Krauzlis-Lisberger (KL) model. We show that the PD model fails to account for the experimentally observed dependence of the eye velocity damping ratio and the oscillation period on the total delay in the feedback loop. To explain the data, a new 'tachometer' feedback model, based on an efference copy signal of eye acceleration, is proposed and analyzed by computer simulation. The model predicts some salient features of monkey pursuit data and suggests a functional role for the extraretinal input to the medial superior temporal area (MST).