  We present a theoretical study of the influence of the nuclear ferromagnetism
on superconductivity in the presence of the electron-nuclear spin interaction.
It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded
in a matrix of ferromagneticaly ordered nuclear spins should manifest the FFLO
(Fulde-Ferel-Larkin-Ovchinniov) state. We outline that the optimal experimental
conditions for observation of FFLO could be achieved by creation, via adiabatic
nuclear demagnetization, of the negative nuclear spin temperatures. In this
case the nuclear polarization points in the opposite to the external magnetic
field direction and the electromagnetic part of the nuclear spin magnetization
compensates the external magnetic field, while the exchange part creates the
nonhomogeneous superconducting order parameter.
