  Phenomenologically viable string vacua may require incorporating Kac-Moody
algebras at level $\geq 2$. We exploit the free fermionic formulation to
construct N=(0,2) world-sheet supersymmetric string models with specific
phenomenological input: N=1 spacetime supersymmetry, three generations of
chiral fermions in gauge groups $SO(10)$ or $SU(5)$, adjoint Higgses, and a
single Yukawa coupling of a fundamental Higgs to the third generation. In this
talk, we will show models of gauge group $SO(10)$ and of $SU(5)$ without any
gauge singlet moduli, and show some novel features appearing in the connection
of these two models. The accompanying, and rather non-trivial, discrete chiral
sub-algebras can determine hierarchies in the fermion mass matrix. Our approach
to string phenomenology opens up the possibility of {\it concrete} explorations
of a wide range of proposals both for dynamical supersymmetry breaking and for
the dynamics of the dilaton and other stringy moduli. (Talk presented at DPF
94, Albuquerque, New Mexico)
