  The Berry phase in a composite system with only one subsystem being driven
has been studied in this Letter. We choose two spin-$\frac 1 2 $ systems with
spin-spin couplings as the composite system, one of the subsystems is driven by
a time-dependent magnetic field. We show how the Berry phases depend on the
coupling between the two subsystems, and what is the relation between these
Berry phases of the whole system and those of the subsystems.
