We present a theoretical treatment of macroscopic quantum self-trapping (MQ
ST) and quantum coherent atomic tunneling in a zero-temperature two-species
Bose-Einstein condensate system in the presence of the nonlinear self-inte
raction of each species, the interspecies nonlinear interaction, and the Jo
sephson-like tunneling interaction. It is shown that the nonlinear interact
ions can dramatically affect the MQST and the atomic tunneling, and lead to
the collapses and revivals (CR) of the population imbalance between the tw
o condensates. The competing effects between the self-interaction of each s
pecies and the interspecies interaction can lead to a quenching of the MQST
and a suppression of the CR and the Shapiro-like steps of the atomic tunne
ling current. It is revealed that interatomic nonlinear interactions can in
duce coherent atomic tunneling between two condensates even though interspe
cies Josephson-like tunneling coupling does not exist.