Super-fluid-to-superfluid phase transitions in a Fermi-liquid leading to th
e emergence of two-gap superfluid states have been studied. The systems of
fermions of one and two (nuclear matter) sorts have been considered. The se
lf-consistent equations describing new two-gap, superfluid states have been
obtained. These equations differ essentially from the equations of the BCS
theory. The solutions of the self-consistent equations corresponding to on
e-gap, and two-gap superfluid states have been found.