The visual pursuit test is a method that collects and analyzes the characteristics of pursuit eye movements and examines the function of the eye movement system. This paper analyzes the model parameters of the smooth pursuit eye movement system in order to explore a method for improving the analysis. The input-output relationship of the smooth pursuit system can be expressed by a quasilinear model. We compute the model parameters (gain, phase, spectral purity, cross covariance) by digital signal processing. Eye movement is recorded by electrooculogram. Both eyes are tested individually. The visual target moves at frequencies of 0.2, 0.4, 0.8, 1.2, and 1.6 Hz. Ranges are gain, 1.01 to 0.70; phase, -0.1 degree to -66 degrees; spectral purity, 0.97 to 0.70; and cross covariance, 0.99 to 0.26. We tested 40 normal subjects as well as patients with ataxia (8), vertigo (18), and ophthalmoplegia (9). The oculomotor system of normal subjects functions as a linear system in the performance of this test at 0.2 to 0.8 Hz. The spectral purity dropped to about 0.70 at 1.6 Hz. The variability of all measures increases greatly at 1.6 Hz, which indicates that this target motion exceeds the tracking ability of many normal subjects and that the oculomotor system of normal subjects functions as a nonlinear system in this condition. Statistical tests show no significant differences between sex, age, and the two eyes. The model parameters tentatively proved effective in clinical application.