  We discuss the effect of the renormalization procedure in the computation of
the unification point for running coupling constants. We explore the effects of
threshold--crossing on the $\beta$--functions. We compute the running of the
coupling constants of the Standard Model, between $m_Z$ and $M_P$, using a mass
dependent subtraction procedure, and then compare the results with $\bar{MS}$,
and with the $\theta$-- function approximation. We also do this for the Minimal
Supersymmetric extension of the Standard Model. In the latter, the bounds on
susy masses that one obtains by requiring perturbative unification are
dependent, to some extent, on the procedure.
