- The paper deals with anomalous phenomena recently observed in operation of models of inductive superconducting current limiters. The anomalies manifest themselves as sharp peaks of voltage or current on the background of a basic AC signal. We demonstrate that these anomalies are observed in AC circuits with models of various current limiters (inductive, hybrid) based on differently processed YBCO elements: sintered ring, melt-textured rings and thin film. It is shown that the nature of these anomalies is self-oscillations appearing in an electric circuit with non-linear superconducting element. The conditions for appearance of these self-oscillations are discussed.