  We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a)
improved Lattice QCD, to two loops in perturbation theory. We employ the
Sheikholeslami-Wohlert (clover) improved action for Wilson fermions.
  The quantity which we study is a typical case of a vacuum expectation value
resulting in an additive renormalization; as such, it is characterized by a
power (linear) divergence in the lattice spacing, and its calculation lies at
the limits of applicability of perturbation theory.
  The dependence of our results on the number of colors $N$, the number of
fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown
explicitly. We compare our results to non perturbative evaluations of
$\kappa_c$ coming from Monte Carlo simulations.
