The theory of the photon drag of dipolar excitons in double-quantum-well nanostructures is presented. It is
shown that the exciton-drag flux density features a resonant behavior if the photon frequency is close to some
transition frequency in the discrete exciton spectrum. When the structure is irradiated with polarized light,
the resonant enhancement of the drag current occurs when the photon energy coincides with the energy of
an excited level of the exciton internal motion and the components of the angular momentum of internal
motion in the initial and final states differ by one. The proposed effect can be used to control exciton transport
in nanostructures based on a two-dimensional exciton gas.