  We discuss some phenomenological aspects of gauged supersymmetric
$\gs$--models on homogeneous coset-spaces $\ESO$ and $SO(10)/U(5)$ which are
some of the most interesting for phenomenology. We investigate in detail the
vacuum configurations of these models, and study the resulting consequences for
supersymmetry breaking and breaking of the internal symmetry. Some
supersymmetric minima for both models with gauged full isometry groups $E_6$
and SO(10) are physically problematic as the Kaehler metric becomes singular
and hence the kinetic terms of the Goldstone boson multiplets vanish. This
leads us to introduce recently proposed soft supersymmetry-breaking mass terms
which displace the minimum away from the singular point. A non-singular Kaehler
metric breaks the linear subgroup $SO(10)\times U(1)$ of the $E_6$ model
spontaneously. The particle spectrum of all these different models is computed.
