Power amplifiers often exhibit undesired behavior from certain input power value which cannot be predicted with a small-signal stability analysis. Among the commonly observed undesired phenomena are spurious oscillations, frequency divisions, hysteresis or chaos. In this contribution, simulation tools are presented, enabling an in-depth study of the origin and characteristics of these phenomena. The developed global stability analysis and stabilization tools have enabled an efficient suppression of the undesired behavior in a switching-mode power amplifier, with minimum degradation of the amplifier performance, in terms of drain efficiency and output power.