In the supersymmetric models with a nontrivial flavor structure in the soft
-breaking sector the exchange of neutral Higgs bosons mediates Delta F=2 tr
ansitions. This mechanism is studied for Delta S,Delta B=2 processes and fo
r a generic form of the soft-breaking terms. We find that Higgs-boson-media
ted FCNC amplitudes increase very rapidly with tan beta and can exceed SUSY
box contribution by up to two orders of magnitude when tan beta similar to
m(t)/m(b). [S0556-2821(99)02505-9].