Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations. Euler angles give a simpler description of the rotations of the eye, and can also be used to formulate an alternative version of the three-dimensional gaze control model. Comparison of the two versions of the model highlights the distinction between the functional predictions of the model, and the predictions which depend only on the choice of mathematical descriptions.