  The propagation of the scalar (\sigma and \delta) and vector (\omega and
\rho) mesons in an iso-asymmetric nuclear matter is studied in detail, using
the Walecka model. We calculate the invariant masses and spectral functions of
the mesons, including the effect of meson mixing. At finite density, the mixing
effect is quite important in the propagation of the scalar and (longitudinal)
vector mesons. In the \sigma channel, we find a three-peak structure in the
spectral function, caused by the mixing effect.
