In stationary head roll positions the eyes are cyclodivergent. We asked whether this phenomenon can be explained by a static hysteresis that differs between the eyes contra- (CE) and ipsilateral (IE) to head roll. Using a motorized turntable, healthy human subjects (N = 8) were continuously rotated about the earth-horizontal naso-occipital axis. Starting from the upright position, a total of three full rotations at a constant velocity (2 °/s) were completed (acceleration = 0.05 °/s², velocity plateau reached after 40 s). Subjects directed their gaze upon a flashing laser dot straight ahead (switched on 20 ms every 2 s). Binocular three-dimensional eye movements were recorded with dual search coils that were modified (wires exiting inferiorly) to minimize torsional artifacts by the eyelids. A sinusoidal function with a first and second harmonic was fitted to torsional eye position as a function of torsional whole-body position at constant turntable velocity. The amplitude and phase of the first harmonic differed significantly between the two eyes (paired t-tests: p < 0.05): on average, counterroll amplitude of IE was larger (CE: 6.6° ± 1.6 SD; IE: 8.1° ± 1.7 SD), while CE showed more position lag relative to the turntable (CE: 12.5° ± 10.7 SD; IE: 5.1° ± 8.7 SD). We conclude that cyclodivergence observed during static ocular counterroll is mainly a result of hysteresis that depends on whether eyes are contra- or ipsilateral to head roll. Static hysteresis also explains the phenomenon of residual torsion, i.e. an incomplete torsional return of the eyes when the first 360° whole-body rotation was completed and subjects were back in upright position (extorsion of CE: 2.0° ± 0.10 SD; intorsion of IE: 1.4° ± 0.10 SD). A computer model that includes asymmetric backlash for each eye can explain dissociated torsional hysteresis during quasi-static binocular counterroll. We hypothesize that ocular torsional hysteresis is introduced at the level of the otolith pathways because the direction-dependent torsional position lag of the eyes is related to the head roll position, not the eye position.