We report here the design and experiments of dual-wideband dual-circularly-polarized (dual-CP) shared-aperture reflectarrays (RAs) operating at K-/Ka-band utilizing a single functional substrate. By coupling the adjacent but separated resonances of H-shaped aperture and circular patch and utilizing the shorted microstrip phase delay lines, the proposed RA cells can offer wideband performance. Then, these RA cells are interleaved in a shared aperture for dual-band operation. By combining the dynamic phase and Berry phase compensation techniques, the RA cells can independently control the reflective phase delay of orthogonal CP beams at both of the targeted bands, providing four degrees of freedom for beamforming. The diffractive property of an infinite periodic gradient array of the interleaved K- and Ka-band cells is investigated, which verifies the wideband performance of the proposed cells. Two RAs with a thin panel thickness of 0.27 and#x03BB;K (and#x03BB;K is the free-space wavelength at K-band) are fabricated and characterized, generating symmetrically- and asymmetrically-distributed dual-wideband dual-CP beams at K-/Ka-band, respectively. The measured bandwidths for the two RAs are wider than 14.1% for K-band right-/left-handed CP beams and about 11% for Ka-band right-/left-handed CP beams with both the gain variation and axial ratio smaller than 2 dB.