  We compute the one-loop gauge couplings in six-dimensional non-Abelian gauge
theories on the T^2/Z_2 orbifold with general GUT breaking boundary conditions.
For concreteness, we apply the obtained general formulae to the gauge coupling
running in a 6D SO(10) orbifold GUT where the GUT group is broken down to the
standard model gauge group up to an extra U(1). We find that the one-loop
corrections depend on the parity matrices encoding the orbifold boundary
conditions as well as the volume and shape moduli of extra dimensions. When the
U(1) is broken by the VEV of bulk singlets, the accompanying extra color
triplets also affect the unification of the gauge couplings. In this case, the
B-L breaking scale compatible with the gauge coupling unification is sensitive
to the change of the compactification scales.
