A consistent evolution of the strong coupling constant $\alpha_s$ from
$M_Z$ to the GUT scale is presented, involving three-loop running and
two-loop decoupling. The two-loop transition from the MS- to the
DR-scheme is properly taken into account. In the second part of
the paper, the bottom quark mass in the DR- scheme at the
electroweak/SUSY scale is evaluated with four-loop accuracy.
We find that the three-loop effects are comparable to the experimental
uncertainty both for $\alpha_s$ and $m_b$.