Abstract: An experimental and theoretical investigation was made of flux jumps and irreversible magnetization curves of mesoscopic Al superconducting rings. In the small magnetic-field region the change of vorticity with magnetic field can be larger than unity. This behavior is connected with the existence of several metastable states of different vorticities. The intentional introduction of a defect in the ring has a large effect on the size of the flux jumps. Calculations based on the time-dependent Ginzburg-Landau model allows us to explain the experimental results semiquantitatively.