Models describing the appearance of an abnormal hysteresis in the critical current of granular superconductors are analyzed. It has been revealed that the most suitable for High T c Superconductors ( H T c S ) is a model based on an irreversibility of the grain surface current that determines the critical current of the Josephson weak links or depairing current of narrow superconducting part in ( H T c S ) oxides. This leads to the irreversibility phenomena in ( H T c S ) at the high magnetic fields H≫ H c1 .