The equations of the PWM voltage-source converter (PWM-VSC) are inherently nonlinear. This paper applies the nonlinear control, associated with A. Isidori, to the unified power flow controller (UPFC). Since the UPFC comprises two PWM-VSCs, this paper is one step further in complexity than the previous application of nonlinear control to the static compensator (STATCOM), which consists of one PWM-VSC. The key in applying nonlinear control is the art of formulating the "Lyapunov function", which fits the bilinear equations of the PWM-VSCs. As the family of controllers of flexible AC transmission systems (FACTS) are based on PWM-VSC, the same key is used to unlock the UPFC.