When visually fixating targets on an isovergence surface, the position of each eye was constrained to a plane. Thus, Listing's law holds during vergence. The planes were, however, rotated temporally with respect to those when viewing distant targets. The effect of this rotation was to produce a torsion which depended on eye elevation; extorsion of the two eyes for downward gaze and intorsion for upward gaze. The saccadic velocity command was relatively unaffected during vergence. Computer simulations suggest that the saccadic tonic command and the vergence command interact multiplicatively in three dimensions.