This letter addresses the cross-polarization properties of electronically controlled multi-phase-center parabolic reflector antennas, illuminated by over-moded primary feeds. Due to the presence of the higher-order modes in the primary feed, the secondary cross-polarization levels deteriorate in the case of symmetric reflector antennas. As for the offset reflectors, the primary multimode feed required to displace the phase-center location may produce a significant crosstalk in the orthogonal polarization. It is shown how one can improve the cross-polarization performances of aforementioned adaptive antennas, which are capable of providing axial beams while their phase-center locations are displaced. The conventional array technique with a simple signal processing is used for the symmetric case, whereas a trimode primary feed is employed for the offset case.