  The nonuniform superconducting state in a ring in which the order parameter
vanishing at one point is studied. This state is characterized by a jump of the
phase by $\pi$ at the point where the order parameter becomes zero. In uniform
rings such a state is a saddle-point state and consequently unstable. However,
for non-uniform rings with e.g. variations of geometrical or physical
parameters or with attached wires this state can be stabilized and may be
realized experimentally.
