  The covariant particle-vibration coupling model within the time blocking
approximation is employed to supplement the Relativistic Random Phase
Approximation (RRPA) with coupling to collective vibrations. The Bethe-Salpeter
equation in the particle-hole channel with an energy dependent residual
particle-hole (p-h) interaction is formulated and solved in the shell-model
Dirac basis as well as in the momentum space. The same set of the coupling
constants generates the Dirac-Hartree single-particle spectrum, the static part
of the residual p-h interaction and the particle-phonon coupling amplitudes.
This approach is applied to quantitative description of damping phenomenon in
even-even spherical nuclei with closed shells $^{208}$Pb and $^{132}$Sn. Since
the phonon coupling enriches the RRPA spectrum with a multitude of
ph$\otimes$phonon states a noticeable fragmentation of giant monopole and
dipole resonances is obtained in the examined nuclei. The results are compared
with experimental data and with results of the non-relativistic approach.
