B -> X_s γ and B^+ -> l^+ ν in the 2HDM type III

We consider the Two Higgs Doublet Model (2HDM) of type III which leads to Flavour Changing Neutral Currents (FCNC) at tree level. In the framework of this model we calculate the NLO contribution for b->s \gamma and the branchings for the meson decays B^+ -> l^+ \nu. We examine the limits on the new parameters \lambda_{bb} and M_{H^\pm}. We take into account the relationship between \lambda_{tt} and \lambda_{bb} coming from the validness of perturbation theory.