For optimal pursuit of a visual target one should avoid rotation about
the line of sight. It is shown that the structure of the optic flow d
uring self-motion imposes certain restrictions on eye and head orienta
tion as a function of the gaze direction, if rotation of the eye about
the line of sight is avoided. These restrictions result in different
strategies for optimal pursuit. Directing the head towards the aim poi
nt of the self-motion in combination with the well known kinematic con
straint on eye movement (Listing's law) is one such possibility.