  Fe-based superconductors (FeSC) exhibit all the properties of systems that
allow the formation of a superconducting phase with oscillating order
parameter, called the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. By the
analysis of the Cooper pair susceptibility in two-band FeSC, such systems are
shown to support the existence of a FFLO phase, regardless of the exhibited
order parameter symmetry. We also show the state with nonzero Cooper pair
momentum, in superconducting FeSC with $\sim \cos(k_{x}) \cdot \cos (k_{y})$
symmetry, to be the ground state of the system in a certain parameter range.
