Oculomotor-plant dynamics are not well characterised, despite their importance for modelling eye-movement control. We analysed the time course of the globe's return after horizontal displacements in three rhesus monkeys lightly anaesthetised with ketamine. The eye-position traces were well fitted by a sum of four exponentials (time constants 0.012, 0.099, 0.46, 7.8 s). The two long time-constant terms accounted for 25% of plant compliance, and led to a model that accounted for hitherto unexplained features of ocular motoneuron firing such as (i) hysteresis, and (ii) the inability of a 2 time-constant model to fit data for both fast and slow eye-movements.