  The evolution of the Dipole Response in nuclei with strong neutron excess is
studied in the Hartree-Fock plus Random Phase Approximation with Skyrme forces.
We find that the neutron excess increases the fragmentation of the isovector
Giant Dipole Resonance, while pushing the centroid of the distribution to lower
energies beyond the mass dependence predicted by the collective models. The
radial separation of proton and neutron densities associated with a large
neutron excess leads to non vanishing isoscalar transition densities to the GDR
states, which are therefore predicted to be excited also by isoscalar nuclear
probes. The evolution of the isoscalar compression dipole mode as a function of
the neutron excess is finally studied. We find that the large neutron excess
leads to a strong concentration of the strength associated with the isoscalar
dipole operator $\sum_ir^3_iY_{10}$, that mainly originates from uncorrelated
excitations of the neutrons of the skin.
