The rotation axis for each of the six extraocular muscles was determined in four eyes from three perfused rhesus monkeys. Measurements of the locations of muscle insertions and origins were made in the stereotaxic reference frame with the x-y plane horizontal and the x-z plane sagittal. The computed rotation axes of the horizontal recti were close to being in the x-z plane at an angle of about 15 degrees to the z axis. The rotation axes of the vertical recti and the obliques were close to being in the x-y plane at an angle of about 30 degrees to the y axis. In five alert rhesus monkeys, we simultaneously recorded extraocular motoneuron activity and eye position in three dimensions (3D). The activity of 51 motoneuron axons was obtained from the oculomotor (n=34), trochlear (n=11), and abducens nerve (n=6) during spontaneous eye movements. To extend the torsional range of eye position, the animals were also put in different static roll positions, which induced ocular counterroll without dynamic vestibular stimulation. Periods of 100 ms during fixation or slow eye movements (<10 degrees/s) were chosen for analysis. For each motoneuron, a multiple linear regression was performed between firing frequency and 3D eye position, expressed as a rotation vector, in both stereotaxic and Listing's reference frame. The direction with the highest correlation coefficient (average R=0.94+/-0.07 SD) was taken as the on-direction. Each unit's activity could be unequivocally attributed to one particular muscle. On-directions for each motoneuron were confined to a well-defined cone in 3D. Average on-directions of motoneurons differed significantly from the corresponding anatomically determined muscle rotation axes expressed in the stereotaxic reference frame (range of deviations: 11.9 degrees to 29.0 degrees). This difference was most pronounced for the vertical recti and oblique muscles. The muscle rotation axes of the vertical rectus pair and the oblique muscle pair form an angle of 58.3 degrees, whereas the corresponding angle for paired motoneuron on-directions was 105.6 degrees. On-directions of motoneurons were better aligned with the on-directions of semicircular canal afferents (range of deviation: 9.4-18.9 degrees) or with the anatomically determined sensitivity vectors of the semicircular canals (range of deviation: 3.9-15.9 degrees) than with the anatomically determined muscle rotation axes, but significant differences remain to be explained. The on-directions of motoneurons were arranged symmetrically to Listing's plane, in the sense that the torsional components for antagonistically paired muscles were almost equal, but of opposite sign. Thus, the torsional components of motoneuron on-directions cancel when eye movements are confined to Listing's plane. This arrangement simplifies the neuronal transformations for conjugate head-fixed voluntary eye movements, while the approximate alignment with the semicircular canal reference frame is optimal for generating compensatory eye movements.