  We study the evolution of (phantom) dark energy universe by taking into
account the higher-order string corrections to Einstein-Hilbert action with a
fixed dilaton. While the presence of a cosmological constant gives stable
de-Sitter fixed points in the cases of heterotic and bosonic strings, no stable
de-Sitter solutions exist when a phantom fluid is present. We find that the
universe can exhibit a Big Crunch singularity with a finite time for type II
string, whereas it reaches a Big Rip singularity for heterotic and bosonic
strings. Thus the fate of dark energy universe crucially depends upon the type
of string theory under consideration.
