A dual mode radar seeker comprising a wide-band passive anti-radar antenna system (3) at the rear of a radome (1), operating at relatively low radar frequencies in an amplitude comparison tracking mode, and a high-frequency (W-band) active amplitude-comparison antenna system (5) in the nose of the radome (1) and having a common boresight with the anti-radar system. The active system employs coarse phase shift steering (31, 41) of the antenna 'beam' for the transmit and, optionally, also, the receive 'beam'. The high frequency and the use of phase shift steering both help to keep down the size of the active radar thus enabling it (5, 7, 9) to be positioned far forward in the nose of the radome (1) so as not to obscure the field of the anti-radar system (3).