Abstract: Hot compression tests of U720Li nickel base superalloy were conducted on a Gleeble-1500D thermal simulating tester. Based on DMM (dynamic material modeling) which proposed by Gegel, different types of instability criteria of Prasad, Gegel, Malas, Murthy, Semiatin were compared and the physical significance of parameters was analyzed. Meanwhile, the processing maps with different instability criteria were obtained. The results showed that the instability does not occur when average power dissipation rate is larger than 40% in the temperature range of 950~1050°C and strain rate range of 5×10^-4~10^-1 s^-1. The deformation condition is appropriate for the processing deformation of superalloy U720Li.