  When relating the strong coupling $\alpha_s$, measured at the scale of the
$Z$ boson mass, to its numerical value at some higher energy, for example the
scale of Grand Unification, it is important to include higher order corrections
both in the running of $\alpha_s$ and the decoupling of the heavy particles. We
compute the two-loop matching coefficients for $\alpha_s$ within the Minimal
Supersymmetric Standard Model (MSSM) which are necessary for a consistent
three-loop evolution of the strong coupling constant. Different scenarios for
the hierarchy of the supersymmetric scales are considered and the numerical
effects are discussed. We find that the three-loop effects can be as large as
and sometimes even larger than the uncertainty induced by the current
experimental accuracy of $\alpha_s(M_Z)$.
