Exciton recurrence motions in double-ring molecular aggregates are investigated using the quantum master equation approach. The rotatory and oscillatory recurrence behaviors are found to be controlled by changing the relative direction of the circular polarization of an incident two-mode laser field. These dynamics are understood by the relative phases among off-diagonal exciton density matrices, the feature of which is determined by the interaction between the circular-polarized field and the degenerate states of the double-ring structure. The results of exciton relaxation effects caused by the exciton−phonon coupling and static disorder also demonstrate the robustness of the exciton recurrence motions in double-ring molecular aggregates.