  We compute the two loop coefficient in the relation between the lattice bare
coupling and the running coupling defined through the Schroedinger functional
for the case of pure SU(2) gauge theory. This result is needed as one
computational component to relate the latter to the MSbar-coupling, and it
allows us to implement O(a) improvement of the Schroedinger functional to
two-loop order. In addition, the two-loop beta-function is verified in a
perturbative computation on the lattice, and the behavior of an improved bare
coupling is investigated beyond one loop.
