  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 $\tan\beta\sim m_t/m_b$.
