  We compute the exact two-loop matching coefficients for the strong coupling
constant alpha_s and the bottom-quark mass m_b within the Minimal
Supersymmetric Standard Model (MSSM), taking into account
  O(alpha_s^2) contributions from Supersymmetric Quantum Chromodynamics (SQCD).
We find that the explicit mass pattern of the supersymmetric particles has a
significant impact on the predictions of alpha_s and m_b at high energies.
Further on, the three-loop corrections exceed the uncertainty due to the
current experimental accuracy. In case of the the running bottom-quark mass,
they can reach in the large tan(beta) regime up to 30% of the tree-level value.
