  The transport properties of a quantum dot coupled to superconducting leads
are analyzed. It is shown that the quasiparticle current in the Kondo regime is
determined by the non-equilibrium dynamics of subgap states (Andreev states)
under an applied voltage. The current at low bias is suppressed exponentially
for decreasing Kondo temperature in agreement with recent experiments. We also
predict novel interference effects due to multiple Landau-Zener transitions
between Andreev states.
