  Supersymmetric gauge theories, in higher dimensions compactified in an
orbifold, give a natural framework to unify the gauge bosons, Higgs fields and
even the matter fields in a single multiplet of the unifying gauge symmetry.
The extra dimensions and the supersymmetry are the two key ingredients for such
an unification. In this work, we investigate various scenarios for the
unification of the three gauge couplings, and the Yukawa couplings in the
Minimal Supersymmetric Standard Model (MSSM), as well as the trilinear Higgs
couplings \lambda and \kappa of the Non-Minimal Supersymmetric Standard Model
(NMSSM). We present an SU(8) model in six dimensions with N=2 supersymmetry,
compactified in a T^2/Z_6 orbifold which unifies the three gauge couplings with
\lambda and \kappa of NMSSM. Then, we present an SU(9) model in 6D, which, in
addition, includes partial unification of Yukawa couplings, either for the
up-type (top quark and Dirac tau-neutrino) or down-type (bottom quark and tau
lepton). We also study the phenomenological implications of these various
unification scenarios using the appropriate renormalization group equations,
and show that such unification works very well with the measured low energy
values of the couplings. The predicted upper bounds for the lightest neutral
Higgs boson mass in our model is higher than those in MSSM, but lower that
those in the general NMSSM (where the couplings \lambda and \kappa are
arbitrary). Some of the predictions of our models can be tested in the upcoming
Large Hadron Collider.
