  We made an analysis of the equations of motion which are obtained from the
one - loop effective action for Brans-Dicke gravity with N dilaton - coupled
massless fermions in a time-dependent conformally flat background. Various
particular solutions, including the well-known stationary one, of the
corresponding set of first-order differential equations are given. Some of
these solutions describe an expanding time-dependent Universe with increasing,
constant or also decreasing dilaton. This is illustrated by a numerical
analysis. For the nonstationary solutions a stability analysis is given.
