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In this paper we propose a method to compute the running top-Yukawa couplingin supersymmetric models with heavy mass spectrum based on the "running" and"decoupling" procedure. In order to enable this approach we compute thetwo-loop SUSY-QCD radiative corrections required in the decoupling process. Themethod has the advantage that large logarithmic corrections are automaticallyresummed through the Renormalization Group Equations. As phenomenologicalapplication we study the effects of this approach on the prediction of thelightest Higgs boson mass at three-loop accuracy. We observe a significantreduction of the renormalization scale dependence as compared to the directmethod, that is based on the conversion relation between the running and polemass for the top quark. The effect of resummation of large logarithmiccontributions consists in an increased prediction for the Higgs boson mass, anobservation in agreement with the previous analyses.

O(\alpha_s^2) corrections to the running top-Yukawa coupling and the mass of the lightest Higgs boson in the MSSM