We discuss the time-dependent brane solutions in higher-dimensional
supergravity theories. We particularly focus on the dynamical extensions of
the intersecting brane solutions involving three branes. We also show that
in the near horizon limits, where the time dependence is negligible, these
branes describe warped AdS spacetimes as in the corresponding static
solutions. We finally examine the lower-dimensional cosmological dynamics
obtained after compactifications of the higher-dimensional solutions and
show the solutions we have found give the four-dimensional universe with
power-law expansion.