An ultra-high pressure high pressure discharge lamp device in which the lamp voltage and the distance between the lamp electrodes can be kept stable is achieved by an operating device supplying an alternating current with rectangular waves to the discharge lamp and control is exercised such that a lower boundary value is set and the operating voltage is increased by reducing the operating frequency of the discharge lamp by a given amount, when the operating voltage of the discharge lamp is below the set lower boundary value. Furthermore, control can also be exercised in such a way that an upper boundary value is set and the operating voltage is reduced by increasing the operating frequency of the discharge lamp by a given amount when the operating voltage of the discharge lamp exceeds the set upper boundary value.