  Quasi-realistic string models in the free fermionic formulation typically
contain an anomalous U(1), which gives rise to a Fayet-Iliopoulos D-term that
breaks supersymmetry at the one--loop level in string perturbation theory.
Supersymmetry is traditionally restored by imposing F- and D-flatness on the
vacuum. By employing the standard analysis of flat directions we present a
quasi--realistic three generation string model in which stringent F- and D-flat
solution do not appear to exist to all orders in the superpotential. We
speculate that this result is indicative of the non-existence of supersymmetric
flat F- and D-solutions in this model. We provide some arguments in support of
this scenario and discuss its potential implications. Bose-Fermi degeneracy of
the string spectrum implies that the one--loop partition function and hence the
one-loop cosmological constant vanishes in the model. If our assertion is
correct, this model may represent the first known example with vanishing
cosmological constant and perturbatively broken supersymmetry. We discuss the
distinctive properties of the internal free fermion boundary conditions that
may correspond to a large set of models that share these properties. The
geometrical moduli in this class of models are fixed due to asymmetric boundary
conditions, whereas absence of supersymmetric flat directions would imply that
the supersymmetric moduli are fixed as well and the dilaton may be fixed by
hidden sector nonperturbative effects.
