  We present a systematic study of accelerating cosmologies obtained from
M/string theory compactifications of hyperbolic spaces with time-varying
volume. A set of vacuum solutions where the internal space is a product of
hyperbolic manifolds is found to give qualitatively the same accelerating
four-dimensional FLRW universe behavior as a single hyperbolic space. We also
examine the possibility that our universe is a hyperbolic space and provide
exact Milne type solutions, as well as intersecting S-brane solutions. When
both the usual 4D spacetime and the m-dimensional internal space are
hyperbolic, we find eternally accelerating cosmologies for $m\geq 7$, with and
without form field backgrounds. In particular, the effective potential for a
magnetic field background in the large 3 dimensions is positive definite with a
local minimum and thus enhances the eternally accelerating expansion.
