The influence of far infrared (FIR) radiation on the tunnel current of GaAs/GaAlAs double-barrier resonant tunnelling structures is investigated both experimentally and theoretically. For a tunnelling process characterized by a transmission coefficient with a full width at half maximum GAMMA(c), which is smaller than the photon energy homegaBAR, a theoretical FIR response which depends on the radiation energy is obtained while, for a tunnelling process with GAMMA(c) larger than homegaBAR, this energy dependence is not observed. Although a clear dependence on the radiation energy could not be observed experimentally we show that a classical rectification cannot explain the obtained FIR response.