A range-sensitive intruder alarm system using FMCW radar. A sinusoidal FMCW signal (14) is generated (11) and mixed (20) with reflected signals (17) to produce an output signal (21) comprising a series of frequency components (f m , 2f m , etc.) which correspond to sidebands of the FMCW signal (14). Each frequency component has a unique amplitude variation with the range of the source of the return signal (17). Selected frequency components (2f m ,5f m ) are filtered (23,24) and their amplitudes compared (28) to define a range limit of the system. The alarm (30,31) is triggered by the output (E) of a threshold circuit (27) which monitors the amplitude of one of the frequency components (2f m ). Triggering of the alarm is inhibited (F) if the comparison (28) reveals a disturbance occurring outside the defined range limit.