Recently, identification systems that use human biometric characteristics in solving the problem of access to information systems are becoming more common. The paper proposes a new method of biometric identification of users of computer systems based on the definition of integral Volterra models of the human oculomotor system (OMS) according to experimental research “input-output” using innovative technology of eye tracking. Developed in the Python IDLE programming environment software to identify OMS. Experimental studies of the OMS of two individuals were performed. Based on the data obtained using the TOBII PRO TX300 eye tracker, the transient functions of the first, second and third orders of the OMS are determined. There is a significant difference in the diagonal intersections of the transition functions of the second and third orders of the two individuals.