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 → sγ and the branchings for the meson decays B+ → l+ν. We examine the limits on the new parameters λbb and M H±. We take into account the relationship between λtt and λbb coming from the validness of perturbation theory.