  Theoretical results for giant resonances in the three doubly magic exotic
nuclei $^{78}$Ni, $^{100}$Sn and $^{132}$Sn are obtained from Hartree-Fock (HF)
plus Random Phase Approximation (RPA) calculations using the D1S
parametrization of the Gogny two-body effective interaction. Special attention
is paid to full consistency between the HF field and the RPA particle-hole
residual interaction. The results for the exotic nuclei, on average, appear
similar to those of stable ones, especially for quadrupole and octupole states.
More exotic systems have to be studied in order to confirm such a trend. The
low energy of the monopole resonance in $^{78}$Ni suggests that the compression
modulus in this neutron rich nucleus is lower than the one of stable ones.
