In a frequency generating system, a triple/single local-oscillator concept for receiving and transmitting in the lower frequency band, transmitting in the upper frequency band, and receiving in the upper frequency band is used for a dual-band transceiver so that a single band-switched VCO can be used as local oscillator for setting the frequency in all four possible operating cases. The system can be used, for example, in highly integrated dual-band mobile parts for GSM 900/1800 mobile radio.