  We calculate the two-loop QCD mixing of the dimension-five flavor-changing
operators that arise in the Standard Model after integrating out the $W$, $Z$
and Higgs bosons and the top-quark, i.e.~the mixing among gluonic and photonic
magnetic moment operators. Our calculation completes the two-loop anomalous
dimension matrix of operators that govern low energy flavor-changing processes.
It is an important ingredient of the next-to-leading calculation of the $B
\rightarrow X_s \gamma$ decay rate.
