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The Higgs-boson production cross section at pp and p p colliders is calculated in QCD at next-to-next-to-leading order (NNLO). We find that the perturbative expansion of the production cross section is well behaved and that scale dependence is reduced relative to the NLO result. These findings give us confidence in the reliability of the prediction. We also report an error in the NNLO correction to Drell-Yan production.