  Effect of the phase fluctuations of the order parameter on the stability of
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly
two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi
surface on the basis of a generalized Ginzburg-Landau theory. It is found that
for the FFLO states with oscillations in a single direction, not only the
long-range order but also quasi-long-range order (QLRO), which is characterized
by a power law decay of the order parameter correlation function, is suppressed
by the phase fluctuations at any finite temperatures. On the other hand, for
the FFLO states with order parameter structures such as triangular and square
lattices, it is shown that the QLRO is possible as the uniform BCS state.
Systems with anisotropy in the Fermi surface and pairing are also discussed.
