  Motivated by recent NMR data suggesting the presence of a
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice in magnetic fields
perpendicular to the superconducting plane in the heavy-fermion superconductor
CeCoIn5, we examine here the stability of FFLO states in quasi two-dimensional
(2D) superconductors under a perpendicular field. It is found that a 3D-like
portion of Fermi surfaces peculiar to CeCoIn5 stabilizes a FFLO vortex state
modulating along the field parallel to the c-axis and that the direction of
modulation in a FFLO vortex lattice is related to the characters of the normal
to FFLO and the Abrikosov to FFLO transitions.
