  We describe the geometric (Berry) phases arising when some quantum systems
are driven by control classical parameters but also by outer classical
stochastic processes (as for example classical noises). The total geometric
phase is then divided into an usual geometric phase associated with the control
parameters and a second geometric phase associated with the stochastic
processes. The geometric structure in which these geometric phases take place
is a composite bundle (and not an usual principal bundle), which is explicitely
built in this paper. We explain why the composite bundle structure is the more
natural framework to study this problem. Finally we treat a very simple example
of a two level atom driven by a phase modulated laser field with a phase
instability described by a gaussian white noise. In particular we compute the
average geometric phase issued from the noise.
