Calculations for the rare decays b -> s gamma and b -> s g, as well as the BB¯-mixing inclusive QCD-corrections in Next-to-Leading-Log-Approximation are presented throughout this work. The decays and the mixing are caused by Flavor Changing Neutral Current (FCNC) processes, which are absent on the tree-level within the framework of the Standard-Model. Hence these processes are qualified to test the validity of the Standard-Model, because possible extensions may provide similar contributions. Considered extensions are the 2-Higgs-Doublet-Model, Left-Right-Models and the Minimal Supersymmetric Standard-Model. It is shown that the determination of the Wilson-coefficients is independent of the treatmentof the light fields for the case of the BB¯-mixing. For this proof the dimensional regularisation of the IR-divergences on one side and a regulator mass for the light fields on the other side isutilized. The well-known value for the mass splitting "Delta m B" available from the BB¯-oscillation is applied to deduce (V td V* tb)². Furthermore the branching ratio BR[B -> "X s gamma"] is calculated within the Standard-Model and the Supersymmetric Standard-Model.