  We study the $N=2$ supersymmetric $E_6$ models on the 6-dimensional
space-time where the supersymmetry and gauge symmetry can be broken by the
discrete symmetry. On the space-time $M^4\times S^1/(Z_2\times Z_2') \times
S^1/(Z_2\times Z_2')$, for the zero modes, we obtain the 4-dimensional $N=1$
supersymmetric models with gauge groups $SU(3)\times SU(2) \times SU(2) \times
U(1)^2$, $SU(4)\times SU(2) \times SU(2) \times U(1)$, and $SU(3)\times SU(2)
\times U(1)^3$ with one extra pair of Higgs doublets from the vector multiplet.
In addition, considering that the extra space manifold is the annulus $A^2$ and
disc $D^2$, we list all the constraints on constructing the 4-dimensional $N=1$
supersymmetric $SU(3)\times SU(2) \times U(1)^3$ models for the zero modes, and
give the simplest model with $Z_9$ symmetry. We also comment on the extra gauge
symmetry breaking and its generalization.
