  We report on the results of a calculation of next-to leading order short
distance QCD corrections to the coefficient $\eta_1$ of the effective $\Delta S
= 2$ Lagrangian in the standard model and discuss the uncertainties inherent in
such a calculation. As a phenomenological application we comment on the
contributions of short distance physics to the ${\rm K}_{\rm L}$--${\rm K}_{\rm
S}$ mass difference. This report is based on research work done in
collaboration with Ulrich Nierste.
