  We study an influence of the continuous measurement in a composite quantum
system C on the evolution of the states of its parts. It is shown that the
character of the evolution (decoherence or recoherence) depends on the type of
the measured quantity and on the initial state of the system. A number of
conditions under which the states of the subsystems of C decohere during the
measuring process are established. We propose a model of the composite system
and specify the observable the measurement of which may result in the
recoherence of the state of one of the subsystems of C. In the framework of
this model we find the optimal regime for the exchange of information between
the parts of C during the measurement. The main characteristics of such a
process are computed. We propose a scheme of detection of the recoherence under
the measurement in a concrete physical experiment.
