  In pure SU(2) gauge theory we compute the two-loop coefficient in the
relation between the lattice bare coupling and the running coupling defined
through the Schroedinger functional. This result is required to relate the
latter to the MSbar-coupling in our programme to compute alpha_s. In addition
it allows us to implement O(a) improvement of the Schroedinger functional to
two-loop order. The two-loop beta-function is verified in a perturbative
computation on the lattice, and the behavior of expansions in the standard and
in the Parisi-improved bare couplings are investigated beyond one loop.
