  We calculate the critical value of the hopping parameter, $\kappa_c$, in
Lattice QCD with Wilson fermions, to two loops in perturbation theory.
  This quantity is an additive renormalization; as such, it is characterized
not only by the standard caveats regarding the asymptotic nature of
perturbative results, but also by a linear divergence in the lattice spacing.
Consequently, our calculation tests rather stringently the limits of
applicability of perturbation theory.
  We compare our results to non perturbative evaluations of $\kappa_c$ coming
from Monte Carlo simulations.
  Finally, we apply a tadpole improvement technique on our results; this shifts
them quite favourably towards the non perturbative values.
