A method and apparatus for operating at least one gas discharge lamp includes supplying a gas discharge lamp with high-frequency alternating voltage from an externally controlled lamp generator having an operating frequency being variable for dimming the gas discharge lamp. The state of the gas discharge lamp is monitored. A preheating phase with an ensuing starting phase are provided for firing the gas discharge lamp. The operating frequency of the lamp generator during the preheating phase is adjusted to be greater than a rated frequency in rated operation. The operating frequency at the beginning of the starting phase is reduced until the gas discharge lamp has attained a predetermined state and the operating frequency is subsequently maintained at least at an instantaneous value thereof until the gas discharge lamp fires. The operating frequency at the end of the starting phase is reduced to the rated frequency, thereby initiating rated operation. The operating frequency is varied for dimming in an ensuing dimming operation.