  We investigate theoretically whether it is feasible to detect $\eta$- and
$\omega$-nucleus bound states. As well as the closed shell nuclei, $^{16}$O,
$^{40}$Ca, $^{90}$Zr and $^{208}$Pb, we also investigate $^6$He, $^{11}$B and
$^{26}$Mg, which are the final nuclei in the proposed experiment involving the
(d,$^3$He) reaction at GSI. Potentials for the $\eta$ and $\omega$ mesons in
these nuclei are calculated in local density approximation, embedding the
mesons in the nucleus described by solving the mean-field equations of motion
in the QMC model. Our results suggest that one should expect to find $\eta$-
and $\omega$-nucleus bound states in all these nuclei.
