The detection of moving targets by a side-looking air- or spaceborne Synthetic Aperture Radar (SAR) is limited due to the bandwidth of the clutter. It has an azimuth spectrum whose bandwidth id determined by the antenna beamwidth in azimuth, the platform speed and the wavelength. Application of the Reflectivity Displacement Method (RDM) allows the detection of moving targets, whose azimuth spectra are within the clutter bandwidth, and also solves the azimuth ambiguity problems of moving targets with high radial velocities. The RDM analyzes the frequency shift between two ground reflectivity functions of adjacent and strongly overlapping azimuth power spectra. It allows the evaluation of the two dimensional Doppler Rate Map from the range compressed radar raw data. By analyzing the Doppler rate map as a function of azimuth and range, one can detect and localize moving targets and evaluate their motion in radial and tangential directions. Experimental results prove the consistency of this method.