  One can define generalized models of gaugino condensation as theories which
dynamically break a discrete R-symmetry, but do not break supersymmetry. We
consider general examples consisting of gauge and matter fields, and the
minimal number of gauge singlet fields to avoid flat directions in the
potential. We explore which R-symmetries can arise, and their spontaneous
breaking. In general, we find that the discrete symmetry is
$\mathbb{Z}_{2b_0R}$ and the number of supersymmetric vacua is $b_0$, where
$b_0$ is the coefficient of the one-loop beta function. Results are presented
for various groups, including $SU(N_c), SO(N_c), Sp(2N_c)$, and $G_2$, for
various numbers of flavors, $N_f$, by several methods. This analysis can also
apply to the other exceptional groups, and thus all simple Lie groups. We also
comment on model building applications where a discrete R-symmetry, broken by
the singlet vevs, can account for $\mu$-type terms and allow a realistic Higgs
spectrum naturally.
