In this paper, the passivity-based approach to controller design for the boost and buck quasi-resonant converters is addressed. Quasi-resonant converters use a soft switching method where the power devices switch at zero voltage or zero current, resulting in low switching loss and high power density. The controller design is carried out using the generalized state space average equations of these converter circuits and the celebrated "energy shaping plus damping injection" ideas of the passivity-based approach. Both direct and indirect output voltage regulation schemes are studied. Simulation results are presented to illustrate the features of the proposed controllers.