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[en] In this thesis the two rare decays B _s→μ"+μ"- and anti B→X_sγ are studied. First the decay B _s→μ"+μ"- is studied within the Standard Model. The three-loop corrections in quantum chromodynamics (QCD) are discussed, and precise Standard-Model predictions for the branching ratio are presented. Then the decay B_s→μ"+μ"- is considered in the type-II 2-Higgs-doublet model, whereby also here the determination of the three-loop correction in QCD is discussed. Thereafter the calculation of the Wilson coefficients for anti B→X_sγ within the Standard Model in three-loop order is discussed. Then the same Wilson coefficients are calculated in 2-Higgs-doublet models in three-loop order. From the predicted decay width by comparison with the experimental data a lower limit for the mass of the charged Higgs boson is derived.