  The evolution equations of the gauge and Yukawa couplings are derived for the
two-loop renormalisation group equations in a five-dimensional SM compactified
on a $S^1/Z_2$ to yield standard four space-time dimensions. Different
possibilities can be discussed, however, we shall consider the limiting case in
which all matter fields are localised on the brane. We will compare our
two-loop results to the results found at one-loop level, and investigate the
evolution of $\sin^2 \theta_W$ in this scenario also.
