  We consider a $D$-dimensional cosmological model with a dilaton field and two
$(D-d-1)$-form field strengths which have nonvanishing fluxes in extra
dimensions. Exact solutions for the model with a certain set of couplings are
obtained by separation of three variables. Some of the solutions describe
accelerating expansion of the $d$-dimensional space. Quantum cosmological
aspects of the model are also briefly mentioned.
