  The recent experimental support for the presence of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the CeCoIn5 directed the
attention towards the mechanisms responsible for this type of
superconductivity. We investigate the FFLO state in a model where
on--site/inter--site pairing coexists with repulsive pair hopping interaction.
The latter interaction is interesting in that it leads to pairing with nonzero
momentum of the Cooper pairs even in the absence of the external magnetic field
(the so-called eta-pairing). It turns out that depending on the strength of the
pair hopping interaction the magnetic field can induce one of two types of the
FFLO phase with different spatial modulations of the order parameter. It is
argued that the properties of the FFLO phase may give information about the
magnitude of the pair hopping interaction. We also show that eta-pairing and
d-wave superconductivity may coexist in the FFLO state. It holds true also for
superconductors which in the absence of magnetic field are of pure d-wave type.
