Accelerating cosmologies and ination in string theories with higher order corrections

We discuss how to obtain inflationary and accelerating cosmological solutions in the context of string theories and M-theory. First, we review the no-go theorem which forbids such solutions in the low-energy effective string theories, i.e. supergravities. Then we show that this can be avoided if we consider time-dependent internal space. This is given by the S-brane solutions in string and M theories. Unfortunately these solutions do not give enough e-folding. We then argue that higher order corrections in string and M theories can give inflationary solutions with big enough e-folding.