  New modes of the magnetic flux penetration in SQUIDs with ferromagnetic
junctions are predicted theoretically. Characteristic multinode anharmonicity
of the current-phase relation implies the coexistence of stable and metastable
0 and $\pi$ states for a large interval of strength of the ferromagnetic
barrier influence at low temperature. As a consequence, the coexistence of
integer and half-integer fluxoid configurations appears in both rf and dc
SQUIDs, and generates two flux jumps per one external flux quantum. In dc
SQUIDs, new flux jumps are manifested as two dips in the critical current
dependence on the external magnetic flux.
