Abstract: 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 nonuniform rings with, e.g., variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.