A measuring system including an oversized cavity resonator operating in the TE01 mode for the determination of the complex permittivity e′- je″ of low-loss liquids at frequencies of about 36 GHz is described. While e′ is obtained by wavelength measurements in the filled and the empty resonator, e″ is determined from the variation of the Q factor of the filled resonator with the length of the dielectric sample. The Q factors of values of about 2·104 to 105 can be measured automatically by means of a desk calculator which controls the frequency and collects the digitized values of the detector output voltage. By means of the calculator, the Q factors of the resonator are determined by fitting analytical (Lorentzian) resonance curves to the measurement data. e″ and the Q factor for zero sample length are calculated according to Gottmann's methods.