  We present the detailed theoretical study of a heterostructure comprising of
two coupled ferromagnetic superconducting layers. Our model may be also
applicable to the layered superconductors with alternating interlayer coupling
in a parallel magnetic field. It is demonstrated that such systems exhibit a
competition between the nonuniform Larkin-Ovchinnikov-Fulde-Ferrel (FFLO) state
and the superconducting state where the sign of the superconducting order
parameter is opposite in adjacent layers. We determine the complete
temperature-field phase diagram both in the cases of low and strong interlayer
coupling. In the former we obtain a new Pi-phase inserted within the FFLO phase
and located close to the usual tricritical point, whereas in the latter the
bilayer in the state reveals a very high paramagnetic limit and the phenomenon
of field-induced superconductivity.
