A series of illusions which occur during pursuit eye movements (pems) and which suggest a complete loss of position constancy during pursuit are discussed. An attempt is made to describe these illusions as instances of an underconstancy of perceived position during gems rather than as a complete loss of constancy. It is suggested that the underconstancy may result from an underregistration of information concerning pem rate which is used by a postulated position constancy mechanism in evaluating retinal image displacement in terms of eye movement information. Supporting evidence is presented and an alternative explanation is briefly considered.