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Hydrogenic donor impurity states in the 2D GaAs=Ga0.7Al0.3As concentric double quantum rings have been investigated under the action of intense laser field. An analytical expression of the effective lateral confinement potential induced by the laser field is obtained. The laser dressed effect has been considered both on electron confining and electron-impurity Coulomb interaction potentials. The single electron energy spectrum and wave functions have been found using the effective mass approximation and exact diagonalization technique. The accidental degeneracy of the impurity states has been observed.