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[docdb]PROBLEM TO BE SOLVED : To provide a lighting device for rare gas discharge lamp capable of stabilizing the change in the photo-quantity of discharge lamp after stopping its operation. SOLUTION : A rare gas discharge lamp D is structured so that a pair of band-shaped external electrodes 5 and 6 are arranged on the peripheral surface of an envelope in such a way as isolated from one another, and a lighting device for this discharge lamp is equipped with a high-frequency voltage generating circuit HC including an output transformer TR having a primary coil TRP and secondary coil TRS and a first switching element S1 in series connection with the primary coil and generating a pulse-form high-frequency voltage on the output side of the output transformer on the basis of the switching operation of the element S1 and a DC/DC converter CV having a function to control the output to approx. a constant power. The DC/DC converter is connected with the input side of the high-frequency voltage generating circuit while the rare gas discharge lamp is connected with the output side, and the power on the input side of this circuit in the condition that the lamp is lighted up, is controlled so as to be approx. constant by the constant power generating function of the DC/DC converter.