  We report on the first microscopic study of the properties of two-phonon
giant resonances in deformed nuclei. The cross sections of the excitation of
the giant dipole and the double giant dipole resonances in relativistic heavy
ion collisions are calculated. We predict that the double giant dipole
resonance has a one-bump structure with a centroid 0.8 MeV higher than twice
energy for the single giant dipole resonance in the reaction under
consideration. The width of the double resonance equals to 1.33 of that for the
single resonance.
