The relativistic Hartree‐Bogoliubov (RHB) model is extended to include density dependent meson‐nucleon vertex functions. Compared with standard relativistic mean‐field effective interactions with nonlinear meson‐exchange terms, the density‐dependent meson‐nucleon couplings provide an improved description of asymmetric nuclear matter, neutron matter and nuclei far from stability. The relativistic random‐phase approximation is employed in the analysis of the evolution of the isovector dipole response in nuclei with large neutron excess, and of the dynamics of isoscalar dipole and compression modes. © 2003 American Institute of Physics