We studied the critical state stability and the dynamics of the ux jumps, caused by thermomagnetic avalanches, in a large (3 × 3 × 1 mm 3 ) single crystal of YBa2Cu3O 7−δ superconductor. Flux jumps were observed only at the lowest temperatures attainable in our system (at about 2.2 K) and for the external magnetic eld parallel to the c-axis of the investigated crystal. It is shown that thermomagnetic avalanches are initiated in dynamic conditions, for which the magnetic diusivity is much smaller than the thermal diusivity. For large single crystals of YBa2Cu3O 7−δ immersed directly in liquid helium, the analysis of the critical state stability can be performed in isothermal approximation. However, the conditions of the critical state stability can change dramatically by improving the thermal isolation between the sample and the surrounding coolant. The dynamics of the ux jumps was analyzed in the framework of the model of magnetic diusion. It is shown that the magnetic diusivity changes dramatically during the process of the thermomagnetic avalanche. We also studied the inuence of the external magnetic eld and of the magnetic history on the duration of the ux jumps.