The detection of moving targets with Synthetic Aperture Radars (SAR) is usually carried out by means of methods based on a Doppler filtering. The targets are detected if their Doppler frequency spectrum falls outside of the clutter spectrum, where the clutter consists, in this case, on the returns from the ground. These methods however present some drawbacks, namely: a) targets with low radial velocity, with respect to the radar, are not detected and, b) in order to create a certain visibility region in the Doppler frequency domain, the Pulse Repetition Frequency (PRF) must be taken sensibly higher than the clutter bandwidth and this entails a reduction of the monitorable swath and then a loss on the possible radar coverage. In order to overcome the afore-mentioned shortcomings, a technique for detecting moving targets whose spectrum is embedded in the clutter spectrum is presented in this paper. The technique is based on the difference in the Doppler frequency rate and spatial correlation between moving and fixed targets. The received signal is first filtered in an adaptive way for improving the power ratio between moving and fixed target. The adaptive filter is then followed by a Doppler-rate filters' bank, each filter being matched to a particular Doppler-rate. The performances of the proposed technique are assessed by means of a simulation program.