  We investigate in stable strange hadronic matter (SHM) the modification of
the masses of the scalar ($\sigma$, $\sigma^*$) and the vector ($\omega$,
$\phi$) mesons. The baryon ground state is treated in the relativistic Hartree
approximation in the nonlinear $\sigma$-$\omega$ and linear $\sigma^*$-$\phi$
model. In stable SHM, the masses of all the mesons reveal considerable
reduction due to large vacuum polarization contribution from the hyperons and
small density dependent effects caused by larger binding.
