Аннотация:The problem of the relative equilibria of a point in the neighborhood of a uniformly rotating homogeneous ball with a spherical cavity is considered. The body rotates about the axis perpendicular to its symmetry axis and passing through its center of mass. Under the assumption of dry friction, the families of nonisolated relative equilibria (libration points) located on the surface of the cavity are studied. Their stability and bifurcations are investigated.