In an antenna system for radio signals in at least two spaced-apart frequency bands above 200 MHz, a quadrifilar helical antenna having an elongate dielectric core with a relative dielectric constant greater than 5 has a conductive sleeve surrounding a proximal part of the core and a longitudinal feeder structure extending through the core to a connection with the helical antenna elements at a distal end of the core. The antenna is operated in an upper frequency band in which it exhibits a first mode of resonance characterized by current maxima at the connections of the helical elements to the feeder structure and at their junctions with the rim of the sleeve, and in a lower frequency band in which the antenna exhibits a second mode of resonance characterized by current minima in the region of the junctions of the helical elements and the sleeve rim. To permit dual mode operation, the antenna system includes an impedance-matching diplexer having filters coupled between a common port for the antenna and further ports for connection to radio signal processing equipment such as a GPS receiver and a mobile telephone operating in the two frequency bands. In the preferred embodiment, the filters and impedance matching elements are formed as microstrip elements on a single substrate.