We discuss the effect of the renormalization prescription in the computation of the unification point for running coupling constants. We explore the effects of threshold crossing on the β functions. We compute the running of the coupling constants of the Standard Model, between mz and Mp, using a mass-dependent subtraction procedure, and then compare the results with MS and with the θ 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.Facultad de Ciencias Exactas