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Superfluid-to-superfluid phase transitions in a Fermi-liquid leading to theemergence of two-gap superfluid states have been studied.  There are considered the systems of fermions of one and two (nuclear matter)sorts. The self-consistent equations describing new two-gap superfluid stateshave been obtained. These equations differ essentially from the equations ofthe BCS theory. The solutions of the self-consistent equations corresponding toone-gap and two-gap superfluid states have been found.Comment: LaTeX2e, 9 pages, 4 figure

Theory of Multi-gap Superfluidity Based on Fermi-liquid Approach