We propose an experiment that would demonstrate nonlinear Josephson-type os
cillations in the relative population of a driven, two-component Bose-Einst
ein condensate. An initial state is prepared in which two condensates exist
in a magnetic trap, each in a different hyperfine state, where the initial
populations and relative phase between condensates can be controlled withi
n experimental uncertainty. A weak driving field is then applied, which cou
ples the two internal states of the atom and consequently transfers atoms b
ack and forth between condensates. We present a model of this system and in
vestigate the effect of the mean field on the dynamical evolution. [S1050-2
947(99)50801-9].