  We consider a late-time cosmological model based on a recent proposal that
the infinite-bare-coupling limit of superstring/M-theory exists and has good
phenomenological properties, including a vanishing cosmological constant, and a
massless, decoupled dilaton. As it runs away to $+ \infty$, the dilaton can
play the role of the quintessence field recently advocated to drive the
late-time accelerated expansion of the Universe. If, as suggested by some
string theory examples, appreciable deviations from General Relativity persist
even today in the dark matter sector, the Universe may smoothly evolve from an
initial "focusing" stage, lasting untill radiation--matter equality, to a
"dragging" regime, which eventually gives rise to an accelerated expansion with
frozen $\Omega(\rm{dark energy})/\Omega(\rm{dark matter})$.
