  We present a detailed study of inflationary solutions in M-theory with higher
order quantum corrections. We first exhaust all exact and asymptotic solutions
of exponential and power-law expansions in this theory with quartic curvature
corrections, and then perform a linear perturbation analysis around fixed
points for the exact solutions in order to see which solutions are more generic
and give interesting cosmological models. We find an interesting solution in
which the external space expands exponentially and the internal space is static
both in the original and Einstein frames. This may be regarded as moduli
stabilization by higher order corrections. Furthermore, we perform a numerical
calculation around this solution and find numerical solutions which give enough
e-foldings. We also briefly summarize similar solutions in type II
superstrings.
