A method and apparatus for operating a high pressure discharge lamp is disclosed. Oscillation in the discharge arc periphery, a problem that occurs with high frequency operation, is eliminated. A high pressure discharge lamp is operated by applying thereto a dc or rectangular wave current to which is superposed an ac component shaped by a high frequency ripple signal that has been amplitude modulated by a modulation signal for inducing instantaneous fluctuations in the power supply input to both ends of the arc gap. The ripple level is thereby temporally varied, and stable operating is possible even exceeding the ripple level at which oscillation in the arc periphery begins.