The tasks of clutter suppression and ground moving target indication are a typical and also very challenging problem for airborne radar systems for both defence and civilian applications. Nowadays, research aims at applying these tasks for passive radar systems on moving platforms. This chapter addresses the problem of clutter cancellation and slowly moving target detection in orthogonal-frequency-division-multiplex-based passive radar systems mounted on moving platforms. Conventional signal processing approaches which exploit multiple receiving channels can be ineffective for the considered application due to the impossibility to control the employed waveform of opportunity. Therefore, a processing scheme, which aims at ground moving target indication needs to address this issue. The space-time adaptive processing scheme, proposed in this Chapter, exploits the benefits of the reciprocal filtering strategy applied at a range compression stage together with a flexible displaced phase center antenna approach. The effectiveness of the proposed scheme is demonstrated via application to a simulated dataset as well as on experimental data collected by a multichannel passive radar on an airborne moving platform.