  The only string models known to reproduce the Minimal Supersymmetric Standard
Model in the low energy effective field theory are those constructed in the
free fermionic formulation. We demonstrate the existence of quasi-realistic
free fermionic heterotic-string models in which supersymmetric singlet flat
directions do not exist. This raises the possibility that supersymmetry is
broken perturbatively in such models by the one-loop Fayet-Iliopoulos term. We
show, however, that supersymmetric flat directions that utilize VEVs of some
non-Abelian fields in the massless string spectrum do exist in the model. We
argue that hidden sector condensates lift the flat directions and break
supersymmetry hierarchically.
