  The presence of an extra dimension of size R\equiv M_c^{-1} introduces
corrections of order (\mu/M_c)\alpha to the gauge and Yukawa couplings and
accelerates their running at scales \mu larger than M_c. This could result in a
grand unification scale M_X\approx 20 M_c. We study the corrections at the
two-loop level. We find corrections of order (\mu/M_c)\alpha^2 for the gauge
couplings and of order (\mu/M_c)^2\alpha^2 for the Yukawa couplings. Therefore,
in the Yukawa sector one and two-loop contributions can be of the same order
below M_X. We show that in the usual scenarios the dominant gauge and Yukawa
couplings are decreasing functions of the scale, in such a way that
(\mu/M_c)\alpha becomes approximately constant and two-loop contributions
introduce just a 30% correction which does not increase with the scale.
