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The calculation of the NNLO QCD corrections to the partonic process gg -> His outlined. For the coupling of the Higgs boson to the gluons we use aneffective Lagrangian in the limit of a heavy top quark. The focus is on theevaluation of the virtual two-loop corrections. It is shown that the leadingpole terms are in agreement with the general formula by Catani.Comment: 3+2 pages, AMS-LaTeX. Talk given by RH at the Meeting of the Division  of Particles and Fields of the American Physical Society (DPF2000), Columbus,  Ohio, August 9--12, 200

HIGGS PRODUCTION IN GLUON FUSION TO ${\mathcal O} (\alpha^4_s)$