Despite their importance for deciphering oculomotor commands, the mechanics of the extraocular muscles and orbital tissues (oculomotor plant) are poorly understood. In particular, the significance of plant non-linearities is uncertain. Here primate plant dynamics were investigated by measuring the eye-movements produced by stimulating the abducens nucleus with brief pulse trains of varying frequency. Statistical analysis of these movements indicated that the effects of stimulation lasted ~40 ms after the final pulse, after which the eye returned passively towards its position before stimulation. Behavior during the passive phase could be approximated by a linear plant model, corresponding to Voigt elements in series, with properties independent of initial eye-position. In contrast behavior during the stimulation phase revealed a sigmoidal relation between stimulation frequency and estimated steady-state tetanic tension, together with a frequency-dependent rate of tension increase, that appeared very similar to the nonlinearities previously found for isometric-force production in primate lateral rectus muscle. These results suggest that the dynamics of the oculomotor plant have an approximately linear component related to steady-state viscoelasticity, and a nonlinear component related to changes in muscle activation. The latter may in part account for the nonlinear relations observed between eye-movement parameters and single-unit firing patterns in the abducens nucleus. These findings point to the importance of recruitment as a simplifying factor for motor control with nonlinear plants.