  We demonstrate that in a wide class of multilayered superconductor -
ferromagnet structures (e.g., S/F, S/F/N and S/F/F') the vanishing Meissner
effect signals the appearance of the in-plane Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) modulated superconducting phase. In contrast to the bulk superconductors
the FFLO instability in these systems can emerge at temperatures close to the
critical one and is effectively controlled by the S layer thickness and the
angle between magnetization vectors in the F/F' bilayers. The predicted FFLO
state reveals through the critical temperature oscillations vs the
perpendicular magnetic field component.
