In a multi-resonance converter for converting a first DC voltage into a second DC voltage, wherein the output of a half-bridge comprising semiconductor switches is connected through a resonance capacitor to the primary winding of a transformer and the secondary winding of the transformer, together with rectifier elements, an output inductor and an output capacitor, forms a current output, it is proposed that a controller, which can be supplied which the voltage across the output capacitor and a reference voltage, should control the semiconductor switches alternately so that one of the semiconductor switches is respectively turned on at a predetermined time after the other semiconductor switch is turned off. Preferably, the frequency is controlled in an upper range of the drawn power while in a lower range of the drawn power, the mark-space ratio is controlled for selected respectively constant frequencies.