We study the coherent atomic tunneling between two zero-temperature Bo
se-Einstein condensates (BEC) confined in a double-well magnetic trap,
Two Gross-Pitaevskii equations For the self-interacting BEC amplitude
s, coupled by a transfer matrix element, describe the dynamics in term
s of the interwell phase difference anti population imbalance. In addi
tion to the anharmonic generalization of the familiar ac Josephson eff
ect and plasma oscillations occurring in superconductor junctions, the
nonlinear BEC tunneling dynamics sustains a self-maintained populatio
n imbalance: a novel ''macroscopic quantum self-trapping'' effect.