A method for processing signals received by a plurality of receiving antennas in a radar system, for example for road safety, which emits sequences of chirp-modulated signals, wherein the received signals are mixed with local replicas of the transmitted signals so as to generate, for each receiving antenna, a sequence of detection signals. The detection signals are subjected to Fourier-transform processing and beam-forming processing for generating values of range, azimuth, and speed for at least one obstacle or “target” detected by the radar system. The method includes an acquisition process for yielding approximate values of range and azimuth of the obstacle, and a tracking process for yielding accurate range, azimuth and speed values of the obstacle itself.