Higgs-mediated FCNC in Supersymmetic Models with Large $\tanβ$

In the supersymmetric models with nontrivial flavour structure in the soft-breaking sector the exchange of neutral Higgses mediates $\Delta F=2$ transitions. This mechanism is studied for $\Delta S, \Delta B=2$ processes and for a generic form of the soft-breaking terms. We find that Higgs-mediated FCNC amplitudes increase very rapidly with $\tan\beta$ and can exceed $SUSY$ box contribution by up to two orders of magnitude when $\tan\beta\sim m_t/m_b$.