  The relativistic random phase approximation is applied in the analysis of the
evolution of the isovector dipole response in nuclei with a large neutron
excess. The self-consistent framework of relativistic mean-field theory, which
has been very successfully applied in the description of ground-state
properties of nuclei far from the valley of $\beta$-stability, is extended to
study the possible onset of low-energy collective isovector dipole modes in
nuclei with extreme isospin values.
