The relativistic random phase approximation is applied in the analysis of t
he evolution of the isovector dipole response in nuclei with a large neutro
n excess. The self-consistent framework of relativistic mean-field theory,
which has been very successfully applied in the description of groundstate
properties of nuclei far from the valley of beta -stability, is extended to
study the possible onset of low-energy collective isovector dipole modes i
n nuclei with extreme isospin values. (C) 2001 Elsevier Science B.V. All ri
ghts reserved.