  We study time-dependent solutions in M and superstring theories with higher
order corrections. We first present general field equations for theories of
Lovelock type with stringy corrections in arbitrary dimensions. We then exhaust
all exact and asymptotic solutions of exponential and power-law expansions in
the theory with Gauss-Bonnet terms relevant to heterotic strings and in the
theories with quartic corrections corresponding to the M-theory and type II
superstrings. We discuss interesting inflationary solutions that can generate
enough e-foldings in the early universe.
