B -> X_s γand B^+ -> l^+ νin the 2HDM type III
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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 γand the branchings for the meson decays B^+ -> l^+ ν. We examine the limits on the new parameters λ_{bb} and M_{H^\pm}. We take into account the relationship between λ_{tt} and λ_{bb} coming from the validness of perturbation theory.