MSSM Higgs Self-Couplings: Two-Loop O(alpha_t alpha_s) Corrections

We analyze the minimal supersymmetric Higgs self-couplings at O(alpha_t alpha_s) within the effective potential approach. The two-loop corrections turn out to be of moderate size in the DRbar scheme if the central scale is chosen as half the SUSY scale. The inclusion of the two-loop corrections reduces the renormalization scale dependence to the per-cent level. These results have a significant impact on measurements of the trilinear Higgs self-couplings at the LHC and a future e^+e^- collider.