1. Kinematic constraints were examined in static eye and head positions after large gaze shifts to visual targets. Three-dimensional eye and head rotations were measured in six adult human subjects by the use of the magnetic field search coil technique. 2. Eye positions in space were found to obey Donder's law; i.e., for any given gaze direction there was a unique three-dimensional orientation. In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface. 3. When only the eye moved (head stationary), the shape of this surface resembled a plane and thus the eye position in space obeyed Listing's law. However, after gaze shifts involving both the eye and the head, the eye in space surface became twisted and thus nonplanar. This twist was similar to that achieved by a Fick gimbal model of rotations in which the horizontal axis is nested within a fixed vertical axis. During oblique gaze shifts, the head made predominantly horizontal movements whereas the eye made predominantly vertical movements. This, combined with the fact that the eye is mounted within the head, causes the eye in space surface to resemble that of a Fick gimbal. 4. The angular position of the head in space was also constrained to a two-dimensional surface. This surface was also not planar (Listinglike) and twisted in a manner similar to that of the eye in space. 5. Whereas the angular position of the eye in head was found to obey Listing's law after head-fixed gaze shifts, violations of Listing's law occurred after head-free gaze shifts. These violations showed significant intersubject variation in their magnitude and character. 6. Given that the eye in space violates Listing's law after head movements, the supposition that Listing's law serves the perceptual purpose of maintaining radial constancy is untenable. The Fick gimballike behavior of the head in space and eye in space may hold several advantages over a Listing's system. When the head in space behaves like a Fick gimbal, a horizontal line through the eyes remains parallel to the horizon. By having the eye in space behave like a Fick gimbal, the work done against gravity may be minimized by having the eye contribute more to vertical gaze shifts than does the head.