The method involves using a high frequency carrier frequency that is frequency modulated with a sweep signal and simultaneously amplitude modulated, whereby a fundamental frequency of the AM signal is first set that is derived from preferably the second longitudinal mode. It involves a preparation stage, conducting a measurement to define a characteristic field given by traversing stepwise varied degrees of AM in a maximum range of 5 to 45 per cant, deriving the optimum degree of AM from lamp impedance variations, searching a frequency associated with the optimal AM and deriving the operating frequency. - Independent claims are also included for the following: - (A) a system with a high-pressure discharge lamp and a voltage adapter - (B) and a voltage adapter.Operating method, electronic ballast and system for resonant operation of high-pressure lamps in the longitudinal mode The operating method is based on the simultaneous use of FM and AM and is distinguished by passing through a number of steps which are used to find an optimum frequency for the AM and, in addition, to define an optimum AM level. An electronic ballast which has a memory module which can be overwritten is used for implementation. The operating method is based on the simultaneous use of FM and AM and is distinguished by passing through a number of steps which are used to find an optimum frequency for the AM and, in addition, to define an optimum AM level. An electronic ballast which has a memory module which can be overwritten is used for implementation.