  We study tunneling dynamics of atomic pairs in Bose-Einstein condensates with
Feshbach resonances. It is shown that the tunneling of the atomic pairs depends
on not only the tunneling coupling between the atomic condensate and the
molecular condensate, but also the inter-atomic nonlinear interactions and the
initial number of atoms in these condensates. It is found that in addition to
oscillating tunneling current between the atomic condensate and the molecular
condensate, the nonlinear atomic-pair tunneling dynamics sustains a self-locked
population imbalance: macroscopic quantum self-trapping effect. Influence of
decoherence induced by non-condensate atoms on tunneling dynamics is
investigated. It is shown that decoherence suppresses atomic-pair tunneling.
