  We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa
matrix. We show that to leading order in the mass and CKM hierarchies the
scaling of the mixings $|V_{ub}|^2$, $|V_{cb}|^2$, $|V_{td}|^2$, $|V_{ts}|^2$
and of the rephase-invariant CP-violating parameter $J$ is universal to all
orders in perturbation theory. In leading order the other CKM elements do not
scale. Imposing the constraint $\lambda _b=\lambda _{\tau}$ at the GUT scale
determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.
