We examine the unsteady flow of a two-phase fluid generated by the nontorsional oscillations of a disk when the disk and the fluid at infinity rotate noncoaxially with the same angular velocity. The solutions are obtained for both the fluid and the particle velocities in closed form. It is found that the solutions remain valid for all values of the frequency of oscillations of the disk including the resonant frequency, which is equal to the angular velocity of rotation. But, in absence of particles, only in the case of resonance no oscillatory solution is possible, which is similar to that of solid-body rotation as pointed out by Thornley (1968). It is also shown that, unlike the case of single-disk configuration, no unique solution exists in a double-disk configuration, a result which is the reverse to that of solid-body rotation. Finally, the results are presented graphically to determine the quantitative response of the particle on the flow.