The models describing the chip and electric systems are usually differential-algebraic equations of high dimension, and the dimension of the equations is too large to be solved effectively by the classical numerical methods such as linear multistep methods and Runge-Kutta methods. To solve these equations, by referencing the A-stability definition of the classical numerical methods of ordinary differential equations, A-stability (strong A-stability) is proposed for waveform relaxation (WR) methods, and the conditions of A-stability (strong A-stability) and non-A-stability and several numerical examples of supporting theoretical results are presented. The obtained results show that WR methods cannot inherit naturally A-stability of underlying numerical methods and one need use A-stable underlying numerical methods and suitable splitting functions for A-stability of WR methods. All these lay a theoretical foundation for constructing the WR methods of stiff systems. Furthermore, B-stability (strong B-stability) of WR methods is proposed by referencing the B-stability definition of the classical numerical methods, and the conditions of the strong B-stability are given.