Behavior of two immiscible liquids of different densities is experimentally investigated in a rotating horizontal cylinder subject to vibrations perpendicular to the axis of rotation. The vibration frequency is comparable to the frequency of rotation. The liquids are centrifuged. The resonant excitation of two-dimensional circular oscillations of light liquid column with respect to the cavity is found. The oscillations can occur both in the direction of the cavity rotation and in the opposite direction and are accompanied, respectively, by a leading or lagging azimuthal motion of the interface relative to the cavity. The existence and direction of the azimuthal motion are determined by the relative frequency of vibrations. The oscillations of the light phase have inertial nature and are caused by the difference in densities of two liquids. The influence of liquids properties on the frequency eigenvalues of circular liquid oscillations and on the intensity of differential rotation is studied. A comparison with the results of other authors who have investigated two-phase cylindrical systems under rotation is made. It is shown that the two-dimensional circular mode of fluid oscillations is typical for rotating two-phase systems as follows from the general character of such parameters as the density ratio and volume ratio.