  We consider a coexistence of two axisymmetric liquid bridges LB_i and LB_m of
two immiscible liquids i and m which are immersed in a third liquid (or gas) e
and trapped between two smooth solid bodies with axisymmetric surfaces S_1,S_2
and free contact lines. Evolution of liquid bridges allows two different
configurations of LB_i and LB_m with multiple (five or three) interfaces of
non-smooth shape. We formulate a variational problem with volume constraints
and present its governing equations supplemented by boundary conditions. We
find a universal relationship between curvature of the interfaces and discuss
the Young relation at the singular curve where all liquids meet together.
