QCD Corrections for the $K^0-\bar K^0$ and $B^0 - \bar B^0$ System

The QCD corrections for the box diagrams are revisited for the case of a heavy top quark with $\mt = 174 \GeV$. We resolve first a longstanding discrepancy between two methods of calculation by showing that they give the same results when the threshold factors are treated correctly. Using this observation we refine our earlier results and derive formulae valid for the $K$- and $B$-meson systems. Our formulae are given in terms of integrals to be evaluated numerically, as well as approximate analytical formulae. These calculations include the evolution above $\MW$ which has been neglected by other authors.