The use of stress-grading systems proved to be essential to suppress corona in the end-turn zone of high voltage machines. Moreover, power dissipation in the end-turn region is believed to be a major factor in the deterioration process of surface field grading systems. This paper introduces two novel techniques for the design and analysis of both linear and nonlinear corona-suppression systems of high voltage machines. The first technique is based on the design of linear stress-grading systems through power-loss minimization and equalization of electric field along the end-turn zone. The second technique is based on the simulation, modeling and analysis of nonlinear stress-grading systems in the time domain using the describing function method. This model generates the time variation of the resistances as well as the surface electric field and potential and ultimately converges to the optimal design parameters of the stress-grading system.