  A fully consistent relativistic RPA calculation is performed for the monopole
and dipole compression modes in nuclei. The emphasis is put on the effects of
Dirac sea states which are generally neglected in relativistic RPA
calculations. It is found that these effects can be quite important for the
isoscalar monopole mode. The main contributions from the pairs of Fermi to
Dirac sea states are through the exchange of the scalar meson, while the vector
mesons play a negligible role. Numerical results of relativistic RPA are
checked with the constrained relativistic mean field model in the monopole
case. A good agreement beteween monopole energies calculated in RRPA and in
time-dependent relativistic mean field approach is achieved. For the monopole
compression mode, a comparison of experimental and calculated energies gives a
value of 250 $\sim$ 270 MeV for the nuclear matter incompressibility. A large
discrepancy remains between theory and experiment in the case of the dipole
compression mode.
