The equilibrium point (EP) hypothesis in the form proposed by A. G. Feldman emphasizes the role of stretch reflex mechanisms in motor control. In Feldman’s formulation, the neuromuscular control variable can be identified as the threshold of the tonic stretch reflex and is denoted by the symbol "l" (lambda). Eye movements are potentially an important test case because the eye movement system has is unique in ways that present a significant challenge for the EP hypothesis. First, it is widely accepted that the extraocular muscles are unique in that they lack any stretch reflexes and so they may violate the basic tenet of the EP hypothesis. Second, saccadic eye movements involve some of the fastest muscle contractions in the human body for which the asymmetric, non-linear viscosity of active muscle (usually neglected in EP models) will have a significant effect on movement kinematics. In addition, reflex time delays (if present for eye movements) would also be expected to have significant effects on kinematics. Finally, unlike other systems, the form of the central commands to ocular motor neurons is well documented and appears to contradict the form of these commands suggested by Feldman. A model of the horizontal eye movement system is presented based on the EP hypothesis and its success in accounting for available data is considered. It is concluded that the EP hypothesis can provide the basis for a realistic model of eye movement control.