Next--to--Leading Order QCD corrections for the $B^0\overline{B^0}$--mixing with an extended Higgs sector

We present a calculation of the B0-B0–mixing including Next–to–Leading Order (NLO) QCD corrections within the Two Higgs Doublet Model (2HDM). The QCD corrections at NLO are contained in the factor denoted by eta_2 which modifies the result obtained at the lowest order of perturbation theory. In the Standard Model case, we confirm the results for eta_2 obtained by Buras, Jamin and Weisz. The factor eta_2 is gauge and renormalization prescription invariant and it does not depend on the infrared behaviour of the theory, which constitutes an important test of the calculations. The NLO–calculations within the 2HDM enhance the LO–result up to 18%, which affects the correlation between M_H and V_{td}.