Although many sufficient conditions for the stability of Takagi-Sugeno-Kang (TSK) fuzzy systems are known, no sufficient instability conditions are available. This paper introduces four sufficient instability tests for type-1 and type-2 TSK fuzzy systems. The first test is developed using a common Lyapunov function. The second test is derived using the Variable Gradient method. The third test is based on the comparison principle with a non-differentiable Lyapunov function candidate and the upper right hand derivative. Finally, the fourth test is obtained using Chetaev's theorem. We provide numerical examples to demonstrate and compare our instability testing.