The physics of critical current inversion (π state of the junction) and enhancement in SFIFS tunnel junctions (S and F are superconducting and ferromagnetic metals, and I is an insulator) is discussed on the basis of a microscopic theory of the proximity effect. The ground state and the critical current of an asymmetric (SF)LI(FS)R junction with a strong ferromagnetic field on one of its “banks” are investigated. It is shown that SFINS junctions with strong magnetism of the F layer are found in a ground state with a ±π/2 difference of the superconducting phases on the banks (N is a normal nonmagnetic metal). The dependence of the dc Josephson effect on temperature and on the angle between the magnetic moments of the F layers in SFIFS junctions is investigated.