Attempts to simulate dysfunction within ocular motor system (OMS) models capable of exhibiting known ocular motor behavior have provided valuable insight into the structure of the OMS required for normal visual function. The pendular waveforms of congenital nystagmus (CN) appear to be quite complex, composed of a sustained sinusoidal oscillation punctuated by braking saccades and foveating saccades followed by periods of extended foveation. Previously, we verified that these quick phases are generated by the same mechanism as voluntary saccades. We propose a computer model of the ocular motor system that simulates the responses of individuals with pendular CN (including its variable waveforms) based on the instability exhibited by the normal pursuit subsystem and its interaction with other components of the normal ocular motor control system. Fixation data from subjects with CN using both infrared and magnetic search coil oculography were used as templates for our simulations. Our OMS model simulates data from individuals with CN during fixation and in response to complex stimuli. The use of position and velocity efference copy to suppress oscillopsia is the key element in allowing for normal ocular motor behavior. The model’s responses to target steps, pulse-steps, ramps, and step-ramps support the hypothetical explanation for the conditions that result in sustained pendular oscillation and the rules for the corrective saccadic responses that shape this underlying oscillation into the well-known family of pendular CN waveforms: pendular (P), pseudopendular (PP), pendular with foveating saccades (P_fs), and pseudopendular with foveating saccades (PP_fs). Position error determined the saccadic amplitudes of foveating saccades, whereas stereotypical braking saccades were not dependent on visual information. Additionally, we propose a structure and method of operation for the fixation subsystem, and use it to prolong the low-velocity intervals immediately following foveating saccades. The model’s robustness supports the hypothesis that the pendular nystagmus seen in CN is due to a loss of damping of the normal pursuit-system velocity oscillation (functionally, it is pursuit-system nystagmus—PSN).