Radial-phase self-oscillations in high-current storage rings are discussed and the conditions for stability are derived for the case of an accelerating system with arbitrary frequency characteristics. A study is made of the interaction of the beam with the accelerating system and with other components of the vacuum vessel at harmonics of the bunch revolution frequency. Results are given of an experimental investigation of the self-excitation of phase oscillations in the storage rings of the Institute of Nuclear Physics of the Siberian section of the U.S.S.R. Academy of Sciences.