  We examine whether a minimal string model possessing the same massless
spectra as the MSSM can be obtained from $Z_4$, $Z_6$ and $Z_8$ orbifold
constructions. Using an anomaly cancellation condition of the target space
duality symmetry, we derive allowable values of a level $k_1$ of U(1)$_Y$ for
the minimal string model on the orbifolds through computer analyses. We
investigate threshold corrections of the gauge coupling constants of SU(3),
  SU(2) and U(1)$_Y$ and examine consistencies of the model with the LEP
experiments. Further we investigate what kinds of hidden sectors are consistent
with the minimal string models. Also their gauge coupling constants of the
hidden groups are estimated. We discuss Yukawa couplings of the models.
