  We classify N=1 orbifolds on the E_6 root lattice and investigate explicit
model constructions on the Z_3xZ_3 orbifold in heterotic string theory.
Interestingly some of the twisted sectors from the Z_3xZ_3 orbifold on the E_6
root lattice have just three fixed tori respectively, and generate three
degenerate massless states. We also found three point functions with flavor
mixing terms. We assume only non-standard gauge embeddings and find that they
lead to three-family SU(5) and SO(10) GUT-like models. These models also
include strongly coupled sectors in the low energy and messenger states charged
with both hidden and visible sectors.
