The current generation of spaceborne Synthetic Aperture Radar (SAR) systems suffers from a trade-off between the achievable spatial resolution and swath width. This has motivated intensive research both on more flexible SAR systems, using multiple transmit/receive channels, and on techniques for removing the ambiguities. Among these techniques, the Azimuth Phase Coding (APC), recently proposed to suppress range ambiguities in conventional SAR systems, stands out for its negligible implementation complexity and its effectiveness for point and distributed ambiguities. This paper investigates the possibility of applying the APC technique to the new, forthcoming generation of multichannel SAR systems, based on Digital Beamforming on receive. The extension of APC to multichannel SAR systems is mathematically described. Specific merit figures are defined to quantify the APC performance. A numerical analysis is developed to characterize the influence on the APC behaviors of the main SAR system parameters. Finally, an example of APC performance is provided, by considering two multichannel SAR systems based on a planar and a reflector antenna.