  A systematic microscopic study of the anharmonic properties of the double
giant dipole resonance (DGDR) has been carried out, for the first time, for
nuclei with mass number $A$ spanning the whole mass table. It is concluded that
the corrections of the energy centroid of the $J^{\pi} = 0^+$ and $2^+$
components of the DGDR from its harmonic limit are negative, have a value of
the order of few hundred keV and follow an $A^{-1}$ dependence.
