  We present a class of dynamical solutions in a D-dimensional gravitational
theory coupled to a dilaton, a form field strength, and a cosmological
constant. We find that for any D due to the presence of a cosmological
constant, the metric of solutions depends on a quadratic function of the brane
world volume coordinates, and the transverse space cannot be Ricci flat except
for the case of 1-branes. We then discuss the dynamics of 1-branes in a
D-dimensional spacetime. For a positive cosmological constant, 1-brane
solutions with D>4 approach the Milne universe in the far-brane region. On the
other hand, for a negative cosmological constant, each 1-brane approaches the
others as the time evolves from a positive value, but no brane collision occurs
for D>4, since the spacetime close to the 1-branes eventually splits into the
separate domains. In contrast, the D=3 case provides an example of colliding
1-branes. Finally, we discuss the dynamics of 0-branes and show that for D>2,
they behave like the Milne universe after the infinite cosmic time has passed.
