Isospin is included in the description of the Coulomb excitation of multipl
e giant isovector dipole resonances. In the excitation of even-even nuclei,
a relevant portion of the excitation strength is shown to be associated wi
th 1(+) two-phonon states, which tends to be hindered or completely suppres
sed in calculations in which the isospin degree of freedom is not considere
d. We find that the excitation cross section is strongly dependent on the g
round state isospin.